Template:A4 honeycombs

This honeycomb is one of seven unique uniform honeycombs constructed by the ${\tilde {A}}_{4}$ Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams:

A4 honeycombs
Pentagon symmetry	Extended symmetry	Extended diagram	Extended group	Honeycomb diagrams
a1	[3[5]]		${\tilde {A}}_{4}$	(None)
i2	[[3[5]]]		${\tilde {A}}_{4}$×2	1, 2, 3,  4, 5, 6
r10	[5[3[5]]]		${\tilde {A}}_{4}$×10	7