Template:A5 honeycombs

This honeycomb is one of 12 unique uniform honeycombs constructed by the [math]\displaystyle{ {\tilde{A}}_5 }[/math] Coxeter group. The extended symmetry of the hexagonal diagram of the [math]\displaystyle{ {\tilde{A}}_5 }[/math] Coxeter group allows for automorphisms that map diagram nodes (mirrors) on to each other. So the various 12 honeycombs represent higher symmetries based on the ring arrangement symmetry in the diagrams:

A5 honeycombs
Hexagon symmetry	Extended symmetry	Extended diagram	Extended group	Honeycomb diagrams
a1	[3[6]]		[math]\displaystyle{ {\tilde{A}}_5 }[/math]
d2	<[3[6]]>		[math]\displaystyle{ {\tilde{A}}_5 }[/math]×21	1, , , ,
p2	[[3[6]]]		[math]\displaystyle{ {\tilde{A}}_5 }[/math]×22	2,
i4	[<[3[6]]>]		[math]\displaystyle{ {\tilde{A}}_5 }[/math]×21×22	,
d6	<3[3[6]]>		[math]\displaystyle{ {\tilde{A}}_5 }[/math]×61
r12	[6[3[6]]]		[math]\displaystyle{ {\tilde{A}}_5 }[/math]×12	3