Small rhombi-tetrahedral-octahedral honeycomb

Small rhombi-tetrahedral-octahedral honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Sratoh
Coxeter diagram	x3o3o *b4x ()
Elements
Cells	2N tetrahedra, N cubes, N small rhombicuboctahedra
Faces	8N triangles, 6N+6N squares
Edges	12N+12N
Vertices	8N
Vertex figure	Triangular frustum, edge lengths 1 (top) and √2 (sides and base)
Measures (edge length 1)
Vertex density	$80-56\sqrt2 \approx 0.80404050711$
Dual cell volume	$\frac{10+7\sqrt2}{16} \approx 1.24371843354$
Related polytopes
Army	Sratoh
Regiment	Sratoh
Dual	Apiculated triangular pyramidal honeycomb
Conjugate	Quasirhombi-tetrahedral-octahedral honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	S4
Convex	Yes

The small rhombi-tetrahedral-octahedral honeycomb, or sratoh, also known as the runcic cubic honeycomb, is a convex uniform honeycomb. 1 tetrahedron, 1 cube, and 3 small rhombicuboctahedra join at each vertex of this honeycomb. It can be formed as an alternated faceting from the cubic honeycomb, alternating a subset of the cubes, or alternately as the birectification of the tetrahedral-octahedral honeycomb.

It can be subdivided into alternating truncated square tiling prism and truncated square tiling alterprism segments.

Representations

A small rhombated tetrahedral-octahedral honeycomb has the following Coxeter diagrams:

• x3o3o *b4x (full symmetry)
• s4o3o4x (as runcic cubic honeycomb)
• qo3xx3oq3oo&#zx

Gallery

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  Wireframe

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External links

• Klitzing, Richard. "sratoh".

• Wikipedia Contributors. "Runcic cubic honeycomb".
• Binnendyk, Eric. "Category 7: Triangular Podiumverts" (#152).