Quarter hypercubic honeycomb
This honeycomb is one of 41 uniform honycombs constructed by the 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 and constructions:
| Extended symmetry |
Extended diagram |
Order | Honeycombs |
|---|---|---|---|
| [31,1,3,3,31,1] | Template:CDD | ×1 | Template:CDD, Template:CDD |
| [[31,1,3,3,31,1]] | Template:CDD | ×2 | Template:CDD, Template:CDD, Template:CDD, Template:CDD |
| <[31,1,3,3,31,1]> = [31,1,3,3,3,4] |
Template:CDD = Template:CDD |
×2 | Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD,
Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD |
| <<[31,1,3,3,31,1]>> = [4,3,3,3,3,4] |
Template:CDD = Template:CDD |
×4 | Template:CDD,Template:CDD,
Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD |
| [<<[31,1,3,3,31,1]>>] = [[4,3,3,3,3,4]] |
Template:CDD = Template:CDD |
×8 | Template:CDD, Template:CDD, Template:CDD, |
References
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