Truncated cubic honeycomb

From Wikipedia, the free encyclopedia

Truncated cubic honeycomb
Type	Uniform honeycomb
Schläfli symbol	t0,1{4,3,4}
Coxeter-Dynkin diagrams
Cell type	3.8.8, {3,4}
Face type	{3}, {4}, {8}
Cells/edge	(3.8.8)4 {3,4}.(3.8.8)2
Faces/edge	{8}4 {3}2.{8}
Cells/vertex	3.8.8 (4) {3,4} (1)
Faces/vertex	{8}4+{3}4
Edges/vertex	5
Euler characteristic	0
Coxeter group	[4,3,4]
Dual	-
Properties	vertex-transitive
Vertex figure Four truncated cubes and one octahedron meet at each vertex in a square pyramid arrangement.

The truncated cubic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is comprised of truncated cubes and octahedra in a ratio of 1:1.

[edit] Symmetry

There is a second uniform colorings by reflectional symmetry of the Coxeter groups:

Construction	bicantellated alternate cubic
Coxeter group	[4,31,1], S3
Picture and Coxeter-Dynkin diagram