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Template:A6 honeycombs - Revision history
2026-07-14T02:47:37Z
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2022-12-15T04:11:22Z
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alpha>Sarika: Created page with "This honeycomb is one of 17 unique uniform honeycombs<ref>* {{mathworld | urlname = Necklace | title = Necklace}}, {{OEIS..."
2022-05-19T10:16:51Z
<p>Created page with "This honeycomb is one of <a href="/index.php?title=Uniform_7-polytope&action=edit&redlink=1" class="new" title="Uniform 7-polytope (page does not exist)">17 unique uniform honeycombs</a><ref>* {{mathworld | urlname = Necklace | title = Necklace}}, {{OEIS..."</p>
<p><b>New page</b></p><div>This honeycomb is one of [[Uniform_7-polytope#Regular_and_uniform_honeycombs|17 unique uniform honeycombs]]<ref>* {{mathworld | urlname = Necklace | title = Necklace}}, {{OEIS el|1=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 />
{| class="wikitable mw-collapsible mw-collapsed"<br />
!colspan=5| A6 honeycombs<br />
|-<br />
![[:File:Symmetries of heptagon.png|Heptagon<BR>symmetry]]<br />
![[Coxeter notation|Extended<BR>symmetry]]<br />
!Extended<BR>diagram<br />
!Extended<BR>group<br />
!Honeycombs<br />
|- style="text-align:center;"<br />
!a1<br />
![3<sup>[7]</sup>]<br />
|{{CDD|node|split1|nodes|3ab|nodes|3ab|branch}}<br />
| <math>{\tilde{A}}_6</math><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 />
|- style="text-align:center;"<br />
!i2<br />
!{{Brackets|3<sup>[7]</sup>}}<br />
|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c3|3ab|branch_c4}}<br />
| <math>{\tilde{A}}_6</math>×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>[[Cyclotruncated 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 />
|- style="text-align:center;"<br />
!r14<br />
![7[3<sup>[7]</sup>]]<br />
|{{CDD|node_c1|split1|nodeab_c1|3ab|nodeab_c1|3ab|branch_c1}}<br />
| <math>{\tilde{A}}_6</math>×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:Article shared content templates]]<br />
</noinclude></div>
alpha>Sarika