Template:D6 honeycombs
Jump to navigation
Jump to search
This honeycomb is one of 41 uniform honeycombs constructed by the <math>{\tilde{D}}_6</math> Coxeter group, all but 6 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 41 permutations are listed with its highest extended symmetry, and related <math>{\tilde{B}}_6</math> and <math>{\tilde{C}}_6</math> constructions:
| D6 honeycombs | |||
|---|---|---|---|
| Extended symmetry |
Extended diagram |
Order | Honeycombs |
| [31,1,3,3,31,1] | ×1 | ||
| [[31,1,3,3,31,1]] | ×2 | ||
| <[31,1,3,3,31,1]> ↔ [31,1,3,3,3,4] |
↔ |
×2 |
|
| <2[31,1,3,3,31,1]> ↔ [4,3,3,3,3,4] |
↔ |
×4 |
|
| [<2[31,1,3,3,31,1]>] ↔ [[4,3,3,3,3,4]] |
↔ |
×8 |
|