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alpha>Sarika: Created page with "This honeycomb is one of 45 unique uniform honeycombs<ref>* {{mathworld | urlname = Necklace | title = Necklace}}, {{OEIS..."
2022-05-19T10:17:21Z
<p>Created page with "This honeycomb is one of <a href="/index.php?title=Uniform_9-polytope&action=edit&redlink=1" class="new" title="Uniform 9-polytope (page does not exist)">45 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_9-polytope#Regular_and_uniform_honeycombs|45 unique uniform honeycombs]]<ref>* {{mathworld | urlname = Necklace | title = Necklace}}, {{OEIS el|1=A000029}} 46-1 cases, skipping one with zero marks</ref> constructed by <br />
the <math>{\tilde{A}}_8</math> [[Coxeter group]]. The symmetry can be multiplied by the ring symmetry of the [[Coxeter diagram]]s: <br />
{| class="wikitable mw-collapsible mw-collapsed"<br />
!colspan=5|A8 honeycombs<br />
|-<br />
![[:File:Regular_enneagon_symmetries.png|Enneagon<BR>symmetry]]<br />
![[Coxeter notation|Symmetry]]<br />
!Extended<BR>diagram<br />
!Extended<BR>group<br />
!Honeycombs<br />
|-<br />
!a1<br />
![3<sup>[9]</sup>]<br />
|{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}<br />
|<math>{\tilde{A}}_8</math><br />
|<br />
{{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes_10lr|3ab|branch}} {{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes|3ab|branch_10l}} {{CDD|node|split1|nodes_11|3ab|nodes|3ab|nodes|3ab|branch_10l}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_10lr|3ab|branch}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes|3ab|branch_10l}} {{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes_10lr|3ab|branch_01l}} {{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes_11|3ab|branch}} <br />
<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch_10l}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_10lr|3ab|branch_01l}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_10lr|3ab|branch_10l}} {{CDD|node|split1|nodes_10lur|3ab|nodes|3ab|nodes_11|3ab|branch_11}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_11|3ab|branch_10l}} {{CDD|node_1|split1|nodes_10lur|3ab|nodes|3ab|nodes_11|3ab|branch_11}} {{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch_10l}}<br />
<br />
|-<br />
!i2<br />
!{{Brackets|3<sup>[9]</sup>}}<br />
|{{CDD|node_c1|split1|nodeab_c2|3ab|nodeab_c3|3ab|nodeab_c4|3ab|branch_c5}}<br />
| <math>{\tilde{A}}_8</math>×2<br />
|<br />
{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}<sub>[[8-simplex honeycomb|1]]</sub> {{CDD|node|split1|nodes_11|3ab|nodes|3ab|nodes|3ab|branch}} <!--{{CDD|node|split1|nodes|3ab|nodes_11|3ab|nodes|3ab|branch}} [×3]--> {{CDD|node|split1|nodes|3ab|nodes|3ab|nodes_11|3ab|branch}} {{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch_11}} <sub>[[Cyclotruncated 8-simplex honeycomb|2]]</sub><br />
<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes|3ab|branch}} {{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes|3ab|branch}} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes_11|3ab|branch}} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch_11}} <br />
<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch}} {{CDD|node|split1|nodes_11|3ab|nodes|3ab|nodes_11|3ab|branch}} {{CDD|node|split1|nodes_11|3ab|nodes|3ab|nodes|3ab|branch_11}} <br />
{{CDD|node|split1|nodes|3ab|nodes_11|3ab|nodes_11|3ab|branch}} {{CDD|node|split1|nodes|3ab|nodes_11|3ab|nodes|3ab|branch_11}} {{CDD|node|split1|nodes|3ab|nodes|3ab|nodes_11|3ab|branch_11}}<br />
<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_11|3ab|branch}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes|3ab|branch_11}} <br />
{{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes_11|3ab|branch}} {{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes|3ab|branch_11}} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes_11|3ab|branch_11}}<br />
<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|3ab|branch}} <!--{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch_11}}--> {{CDD|node|split1|nodes_11|3ab|nodes|3ab|nodes_11|3ab|branch_11}} {{CDD|node|split1|nodes|3ab|nodes_11|3ab|nodes_11|3ab|branch_11}} <br />
<br />
{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|3ab|branch}} {{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch_11}} {{CDD|node_1|split1|nodes_11|3ab|nodes|3ab|nodes_11|3ab|branch_11}} {{CDD|node_1|split1|nodes|3ab|nodes_11|3ab|nodes_11|3ab|branch_11}} <br />
<br />
{{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|3ab|branch_11}} <br />
<br />
|-<br />
!i6<br />
![3[3<sup>[9]</sup>]]<br />
|{{CDD|node_c3|split1|nodeab_c1|3ab|nodeab_c1|3ab|nodeab_c3|3ab|branch_c1}}<br />
| <math>{\tilde{A}}_8</math>×6<br />
| {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes_11|3ab|branch}} {{CDD|node|split1|nodes_11|3ab|nodes_11|3ab|nodes|3ab|branch_11}}<br />
<br />
|-<br />
!r18<br />
![9[3<sup>[9]</sup>]]<br />
|{{CDD|node_c1|split1|nodeab_c1|3ab|nodeab_c1|3ab|nodeab_c1|3ab|branch_c1}}<br />
| <math>{\tilde{A}}_8</math>×18<br />
|{{CDD|node_1|split1|nodes_11|3ab|nodes_11|3ab|nodes_11|3ab|branch_11}} <sub>[[Omnitruncated 8-simplex honeycomb|3]]</sub><br />
|}<noinclude><br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Article shared content templates]]<br />
</noinclude></div>
alpha>Sarika