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Symmetric probability distribution - Revision history
2026-06-09T02:18:46Z
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en>Glenbarnett: /* Properties */ added "(if they exist)" to assertion about odd moments
2013-10-29T02:21:19Z
<p><span class="autocomment">Properties: </span> added "(if they exist)" to assertion about odd moments</p>
<p><b>New page</b></p><div>This honeycomb is one of [[Uniform_polyexon#Regular_and_uniform_honeycombs|17 unique uniform honeycombs]]<ref>* {{mathworld | urlname = Necklace | title = Necklace}}, [http://oeis.org/A000029 A000029] 18-1 cases, skipping one with zero marks</ref> constructed by <br />
the <math>{\tilde{A}}_6</math> [[Coxeter group]], grouped by their extended symmetry of the [[Coxeter–Dynkin diagram]]s: <br />
<br />
{| class=wikitable<br />
!Heptagon<BR>symmetry<br />
![[Coxeter notation|Extended<BR>symmetry]]<br />
!Extended<BR>diagram<br />
!Extended<BR>order<br />
!Honeycombs<br />
|- align=center<br />
!a1<br />
![3<sup>[7]</sup>]<br />
|{{CDD|node|split1|nodes|3ab|nodes|3ab|branch}}<br />
| ×1<br />
|<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|branch_10l}} <br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|branch_10l}} <br />
|- align=center<br />
!i2<br />
!<nowiki>[[</nowiki>3<sup>[7]</sup>]]<br />
|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c3|3ab|branch_c4}}<br />
| ×2<br />
|<br />
{{CDD|node_1|split1|nodes|3ab|nodes|3ab|branch}}<sub>[[6-simplex honeycomb|1]]</sub><br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|branch}}<br />
{{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|branch}} <br />
{{CDD|node_1|split1|nodes|3ab|nodes|3ab|branch_11}} <br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|branch}}<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|branch_11}}<br />
{{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|branch_11}}<br />
<br />
{{CDD|node|split1|nodes_11|3ab|nodes|3ab|branch}} <br />
{{CDD|node|split1|nodes|3ab|nodes_11|3ab|branch}}<br />
{{CDD|node|split1|nodes|3ab|nodes|3ab|branch_11}}<sub>[[Truncated 6-simplex honeycomb|2]]</sub><br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|branch}} <br />
{{CDD|node|split1|nodes_11|3ab|nodes|3ab|branch_11}}<br />
{{CDD|node|split1|nodes|3ab|nodes_11|3ab|branch_11}}<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|branch_11}}<br />
|- align=center<br />
!r14<br />
![7[3<sup>[7]</sup>]]<br />
|{{CDD|node_c1|split1|nodeab_c1|3ab|nodeab_c1|3ab|branch_c1}}<br />
| ×14<br />
|<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|branch_11}}<sub>[[Omnitruncated 6-simplex honeycomb|3]]</sub><br />
|}<noinclude><br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Encyclopedic content templates]]<br />
</noinclude></div>
en>Glenbarnett