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:

D6 honeycombs
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
<2[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, Template:CDD, Template:CDD
[<2[31,1,3,3,31,1]>] ↔ [[4,3,3,3,3,4]]	Template:CDD ↔ Template:CDD	×8	Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD