Template:D5 honeycombs

This honeycomb is one of 20 uniform honeycombs constructed by the ${\tilde{D}}_5$ 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:

D5 honeycombs
Extended symmetry	Extended diagram	Extended group	Honeycombs
[31,1,3,31,1]	Template:CDD	${\tilde{D}}_5$	Template:CDD
<[31,1,3,31,1]> ↔ [31,1,3,3,4]	Template:CDD ↔ Template:CDD	${\tilde{D}}_5$×21 = ${\tilde{B}}_5$	Template:CDD, Template:CDD, Template:CDD, Template:CDD Template:CDD, Template:CDD, Template:CDD, Template:CDD
[[31,1,3,31,1]]	Template:CDD	${\tilde{D}}_5$×22	Template:CDD, Template:CDD
<2[31,1,3,31,1]> ↔ [4,3,3,3,4]	Template:CDD ↔ Template:CDD	${\tilde{D}}_5$×41 = ${\tilde{C}}_5$	Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD, Template:CDD
[<2[31,1,3,31,1]>] ↔ [[4,3,3,3,4]]	Template:CDD ↔ Template:CDD	${\tilde{D}}_5$×8 = ${\tilde{C}}_5$×2	Template:CDD, Template:CDD, Template:CDD