Template:A7 honeycombs

This honeycomb is one of 29 unique uniform honeycombs constructed by the [math]\displaystyle{ {\tilde{A}}_7 }[/math] 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]]		[math]\displaystyle{ {\tilde{A}}_7 }[/math]
d2	<[3[8]]>		[math]\displaystyle{ {\tilde{A}}_7 }[/math]×21	1
p2	[[3[8]]]		[math]\displaystyle{ {\tilde{A}}_7 }[/math]×22	2
d4	<2[3[8]]>		[math]\displaystyle{ {\tilde{A}}_7 }[/math]×41
p4	[2[3[8]]]		[math]\displaystyle{ {\tilde{A}}_7 }[/math]×42
d8	[4[3[8]]]		[math]\displaystyle{ {\tilde{A}}_7 }[/math]×8
r16	[8[3[8]]]		[math]\displaystyle{ {\tilde{A}}_7 }[/math]×16	3