Template:A7 honeycombs

This honeycomb is one of 29 unique uniform honeycombs^[1] constructed by the ${\displaystyle {\tilde {A}}_{7}}$ Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:

A7 honeycombs
Octagon symmetry	Extended symmetry	Extended diagram	Extended group	Honeycombs
a1	[3[8]]		${\displaystyle {\tilde {A}}_{7}}$
d2	<[3[8]]>		${\displaystyle {\tilde {A}}_{7}}$×21	1
p2	[[3[8]]]		${\displaystyle {\tilde {A}}_{7}}$×22	2
d4	<2[3[8]]>		${\displaystyle {\tilde {A}}_{7}}$×41
p4	[2[3[8]]]		${\displaystyle {\tilde {A}}_{7}}$×42
d8	[4[3[8]]]		${\displaystyle {\tilde {A}}_{7}}$×8
r16	[8[3[8]]]		${\displaystyle {\tilde {A}}_{7}}$×16	3