Small rhombi-tetrahedral-octahedral honeycomb

Small rhombi-tetrahedral-octahedral honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Sratoh
Coxeter diagram	x4o3x2o3*b ()
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
Dual cell volume
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
Nature	Tame

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.

Vertex coordinates[edit | edit source]

The vertices of a small rhombi-tetrahedral-octahedral honeycomb of edge length 1, centered at a small rhombicuboctahedron, are given by all permutations of:

$\left(\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})i,\,\pm {\frac {1}{2}}+(2+{\sqrt {2}})j,\,\pm {\frac {1}{2}}+(2+{\sqrt {2}})k\right),$
$\left(\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})i,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})j,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(2+{\sqrt {2}})k\right),$