Difference between revisions of "Template:D4 honeycombs"
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imported>JJMC89 bot III m (Moving Category:Encyclopedic content templates to Category:Article shared content templates per Wikipedia:Categories for discussion/Log/2020 October 26#Category:Encyclopedic content templates) |
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|{{CDD|node_1|3|node|splitsplit1|branch3|node}}[[16-cell honeycomb|<sub>3</sub>]], {{CDD|node_1|3|node_1|splitsplit1|branch3|node}} [[Truncated 16-cell honeycomb|<sub>4</sub>]], {{CDD|node|3|node|splitsplit1|branch3_11|node_1}} [[Birectified 16-cell honeycomb|<sub>5</sub>]], {{CDD|node|3|node_1|splitsplit1|branch3_11|node_1}} [[Bitruncated 16-cell honeycomb|<sub>6</sub>]] | |{{CDD|node_1|3|node|splitsplit1|branch3|node}}[[16-cell honeycomb|<sub>3</sub>]], {{CDD|node_1|3|node_1|splitsplit1|branch3|node}} [[Truncated 16-cell honeycomb|<sub>4</sub>]], {{CDD|node|3|node|splitsplit1|branch3_11|node_1}} [[Birectified 16-cell honeycomb|<sub>5</sub>]], {{CDD|node|3|node_1|splitsplit1|branch3_11|node_1}} [[Bitruncated 16-cell honeycomb|<sub>6</sub>]] | ||
|- style="text-align:center;" | |- style="text-align:center;" | ||
| − | |[4[<sup>1,1</sup>3<sup>1,1</sup>]]<BR>↔ [< | + | |[4[<sup>1,1</sup>3<sup>1,1</sup>]]<BR>↔ [<nowiki/>[4,3,3,4]] |
|{{CDD|nodeab_c1|split2|node_c2|split1|nodeab_c1}}<BR>↔ {{CDD|node|4|node_c1|3|node_c2|3|node_c1|4|node}} | |{{CDD|nodeab_c1|split2|node_c2|split1|nodeab_c1}}<BR>↔ {{CDD|node|4|node_c1|3|node_c2|3|node_c1|4|node}} | ||
| <math>{\tilde{D}}_4</math>×8 = <math>{\tilde{C}}_4</math>×2 | | <math>{\tilde{D}}_4</math>×8 = <math>{\tilde{C}}_4</math>×2 | ||
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{{reflist}} | {{reflist}} | ||
| − | [[Category: | + | [[Category:Article shared content templates]] |
</noinclude> | </noinclude> | ||
Latest revision as of 19:28, 3 November 2020
There are ten uniform honeycombs constructed by the <math>{\tilde{D}}_4</math> Coxeter group, all repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 10th is constructed as an alternation. As subgroups in Coxeter notation: [3,4,(3,3)*] (index 24), [3,3,4,3*] (index 6), [1+,4,3,3,4,1+] (index 4), [31,1,3,4,1+] (index 2) are all isomorphic to [31,1,1,1].
The ten permutations are listed with its highest extended symmetry relation: