Trinomial triangle
This honeycomb is one of 20 uniform honycombs constructed by the 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:
Extended symmetry |
Extended diagram |
Order | Honeycombs |
---|---|---|---|
[31,1,3,31,1] | Template:CDD | ×1 | Template:CDD |
[[31,1,3,31,1]] | Template:CDD | ×2 | Template:CDD, Template:CDD |
<[31,1,3,31,1]> = [31,1,3,3,4] |
Template:CDD = Template:CDD |
×2 | Template:CDD, Template:CDD, Template:CDD, Template:CDD |
<<[31,1,3,31,1]>> = [4,3,3,3,4] |
Template:CDD = Template:CDD |
×4 | Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD |
[<<[31,1,3,1,1]>>] = [[4,3,3,3,4]] |
Template:CDD = Template:CDD |
×8 | Template:CDD, Template:CDD, Template:CDD |
References
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