Small rhombitetrahedraloctahedral honeycomb
Small rhombitetrahedraloctahedral 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  Quasirhombitetrahedraloctahedral honeycomb 
Abstract & topological properties  
Orientable  Yes 
Properties  
Symmetry  S_{4} 
Convex  Yes 
Nature  Tame 
The small rhombitetrahedraloctahedral 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 tetrahedraloctahedral 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 rhombitetrahedraloctahedral honeycomb of edge length 1, centered at a small rhombicuboctahedron, are given by all permutations of:
where i, j, and k range over the integers.
Representations[edit  edit source]
A small rhombated tetrahedraloctahedral honeycomb has the following Coxeter diagrams:
 x4o3x2o3*b () (full symmetry)
 s4o3o4x () (as runcic cubic honeycomb)
 qo3xx3oq3oo&#zx
Gallery[edit  edit source]

Wireframe

External links[edit  edit source]
 Klitzing, Richard. "sratoh".
 Wikipedia contributors. "Runcic cubic honeycomb".
 Binnendyk, Eric. "Category 7: Triangular Podiumverts" (#152).