Truncated cubic honeycomb

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Truncated cubic honeycomb
Type Uniform honeycomb
Schläfli symbol t0,1{4,3,4}
Coxeter-Dynkin diagrams Image:CDW_ring.pngImage:CDW_4.pngImage:CDW_ring.pngImage:CDW_3.pngImage:CDW_dot.pngImage:CDW_4.pngImage:CDW_dot.png
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
Image:VF-truncated cubic.png
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

Image:CD_ring.pngImage:CD_4.pngImage:CD_3b.pngImage:CD_downbranch-10.pngImage:CD_3b.pngImage:CD_dot.png
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