Template:D6 honeycombs

This honeycomb is one of 41 uniform honeycombs constructed by the $${\tilde{D}}_6$$ 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 $${\tilde{B}}_6$$ and $${\tilde{C}}_6$$ constructions: