Chaplygin sleigh

This honeycomb is one of 77 uniform honycombs constructed by the ${\tilde{D}}_7$ Coxeter group, all but 10 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 77 permutations are listed with its highest extended symmetry, and related ${\tilde{B}}_7$ and ${\tilde{C}}_7$ constructions:

Extended symmetry	Extended diagram	Order	Honeycombs
[31,1,3,3,3,31,1]	Template:CDD	×1	Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD,
[[31,1,3,3,3,31,1]]	Template:CDD	×2	Template:CDD, Template:CDD, Template:CDD, Template:CDD
<[31,1,3,3,3,31,1]> = [31,1,3,3,3,3,4]	Template:CDD = Template:CDD	×2
<<[31,1,3,3,3,31,1]>> = [4,3,3,3,3,3,4]	Template:CDD = Template:CDD	×4
[<<[31,1,3,3,3,31,1]>>] = [[4,3,3,3,3,3,4]]	Template:CDD = Template:CDD	×8

References

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