Order-5 cubic honeycomb

Order-5 cubic honeycomb
Rank	4
Dimension	3
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.

Related polytopes[edit | edit source]

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

v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
Dodecahedral honeycomb	doehon	${5,3,4}$
Rectified dodecahedral honeycomb	riddoh	r ${5,3,4}$
Rectified order-5 cubic honeycomb	ripech	r ${4,3,5}$
Order-5 cubic honeycomb	pechon	${4,3,5}$
Truncated dodecahedral honeycomb	tiddoh	t ${5,3,4}$
Small rhombated dodecahedral honeycomb	sriddoh	rr ${5,3,4}$
Small prismated dodecahedral honeycomb	sidpicdoh	t_0,3 ${5,3,4}$
Cubic-dodecahedral honeycomb	ciddoh	2t ${5,3,4}$
Small rhombated order-5 cubic honeycomb	sripech	rr ${4,3,5}$
Truncated order-5 cubic honeycomb	tipech	t ${4,3,5}$
Great rhombated dodecahedral honeycomb	griddoh	tr ${5,3,4}$
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 rhombated order-5 cubic honeycomb	gripech	tr ${4,3,5}$
Great prismated dodecahedral honeycomb	gidpicdoh	t_0,1,2,3 ${5,3,4}$
Order-5 demicubic honeycomb	phachon	s ${5,3,4}$
Truncated order-5 demicubic honeycomb	tophach
Small rhombated order-5 demicubic honeycomb	sirphach
Great rhombated order-5 demicubic honeycomb	girphach