Order-5 cubic honeycomb

Order-5 cubic honeycomb
Rank	4
Type	Regular, compact
Space	Hyperbolic
Notation
Bowers style acronym	Pechon
Coxeter diagram	o5o3o4x ()
Schläfli symbol	{4,3,5}
Elements
Cells	5N cubes
Faces	15N squares
Edges	12N
Vertices	2N
Vertex figure	Icosahedron, edge length √2
Measures (edge length 1)
Circumradius
Related polytopes
Army	Pechon
Regiment	Pechon
Dual	Dodecahedral honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	[5,3,4]
Convex	Yes

The order-5 cubic honeycomb is a compact regular tiling of 3D hyperbolic space. 5 cubes meet at an edge, and 20 meet at a vertex.

This honeycomb can be alternated to produce the alternated order-5 cubic honeycomb, which is uniform.

Related polytopes[edit | edit source]

o5o3o4o truncations
Name	OBSA	Schläfli symbol
Dodecahedral honeycomb	doehon	{5,3,4}
Truncated dodecahedral honeycomb	tiddoh	t{5,3,4}
Rectified dodecahedral honeycomb	riddoh	r{5,3,4}
Cubic-dodecahedral honeycomb	ciddoh	2t{5,3,4}
Rectified order-5 cubic honeycomb	ripech	r{4,3,5}
Truncated order-5 cubic honeycomb	tipech	t{4,3,5}
Order-5 cubic honeycomb	pechon	{4,3,5}
Small rhombated dodecahedral honeycomb	sriddoh	rr{5,3,4}
Great rhombated dodecahedral honeycomb	griddoh	tr{5,3,4}
Small rhombated order-5 cubic honeycomb	sripech	rr{4,3,5}
Great rhombated order-5 cubic honeycomb	gripech	tr{4,3,5}
Small prismated dodecahedral honeycomb	sidpicdoh	t_0,3{5,3,4}
Prismatorhombated order-5 cubic honeycomb	pripech	t_0,1,3{5,3,4}
Prismatorhombated dodecahedral honeycomb	priddoh	t_0,1,3{4,3,5}
Great prismated dodecahedral honeycomb	gidpicdoh	t_0,1,2,3{5,3,4}