Truncated tetrahedral-octahedral honeycomb

Truncated tetrahedral-octahedral honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Tatoh
Coxeter diagram
Elements
Cells	2N truncated tetrahedra, N cuboctahedra, N truncated octahedra
Faces	8N triangles, 6N squares, 8N hexagons
Edges	6N+24N
Vertices	12N
Vertex figure	Rectangular pyramid, base edge lengths 1 and √2, side edge lengths √3
Measures (edge length 1)
Vertex density	$\frac{4\sqrt2}9 \approx 0.62853936105$
Dual cell volume	$\frac{9\sqrt2}8 \approx 1.59099025767$
Related polytopes
Army	Tatoh
Regiment	Tatoh
Dual	Rhombic pyramidal honeycomb
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	S4
Convex	Yes

The truncated tetrahedral-octahedral honeycomb, or tatoh, also known as the cantic cubic honeycomb, is a convex uniform honeycomb. 1 cuboctahedron, 2 truncated octahedra, and 2 truncated tetrahedra join at each vertex of this honeycomb. As one of its names suggests, it can be formed by truncation of the tetrahedral-octahedral honeycomb, or as an alternated faceting from the small rhombated cubic honeycomb.

Representations

A truncated tetrahedral-octahedral honeycomb has the following Coxeter diagrams:

• (full symmetry)
• (P4 symmetry, as truncated cyclotetrahedral honeycomb)
• (as cantic cubic honeycomb)

Gallery

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  Wireframe

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External links

• Klitzing, Richard. "tatoh".

• Wikipedia Contributors. "Cantic cubic honeycomb".
• Binnendyk, Eric. "Category 2: Truncates" (#16).