Template:A8 honeycombs

This honeycomb is one of 45 unique uniform honeycombs^[1] constructed by the ${\tilde{A}}_{8}$ Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:

A8 honeycombs
Enneagon symmetry	Symmetry	Extended diagram	Extended group	Honeycombs
a1	[3^[9]]	Template:CDD	${\tilde{A}}_{8}$	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
i2	Template:Brackets	Template:CDD	${\tilde{A}}_{8}$ ×2	Template:CDD₁ Template:CDD 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 Template:CDD Template:CDD Template:CDD Template:CDD Template:CDD Template:CDD Template:CDD Template:CDD
i6	[3[3^[9]]]	Template:CDD	${\tilde{A}}_{8}$ ×6	Template:CDD Template:CDD
r18	[9[3^[9]]]	Template:CDD	${\tilde{A}}_{8}$ ×18	Template:CDD ₃

References

↑ * Template:Mathworld, Template:OEIS el 46-1 cases, skipping one with zero marks