Template:D5 honeycombs
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This honeycomb is one of 20 uniform honeycombs constructed by the <math>{\tilde{D}}_5</math> Coxeter group, all but 3 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 20 permutations are listed with its highest extended symmetry relation:
| D5 honeycombs | |||
|---|---|---|---|
| Extended symmetry |
Extended diagram |
Extended group |
Honeycombs |
| [31,1,3,31,1] | <math>{\tilde{D}}_5</math> | ||
| <[31,1,3,31,1]> ↔ [31,1,3,3,4] |
↔ |
<math>{\tilde{D}}_5</math>×21 = <math>{\tilde{B}}_5</math> |
|
| [[31,1,3,31,1]] | <math>{\tilde{D}}_5</math>×22 | ||
| <2[31,1,3,31,1]> ↔ [4,3,3,3,4] |
↔ |
<math>{\tilde{D}}_5</math>×41 = <math>{\tilde{C}}_5</math> | |
| [<2[31,1,3,31,1]>] ↔ [[4,3,3,3,4]] |
↔ |
<math>{\tilde{D}}_5</math>×8 = <math>{\tilde{C}}_5</math>×2 | |