Difference between revisions of "Template:D4 honeycombs"
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imported>Tomruen |
imported>Izno (clean tags) |
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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 | ||
Revision as of 00:16, 17 May 2016
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: