Truncated octahedral prism

The truncated octahedral prism or tope is a prismatic uniform polychoron that consists of 2 truncated octahedra, 6 cubes, and 8 hexagonal prisms. Each vertex joins 1 truncated octahedron, 1 cube, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated octahedron. As such it is also a convex segmentochoron (designated K-4.89 on Richard Klitzing's list).

This polychoron can be alternated into a pyritohedral icosahedral antiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a truncated octahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
 * $$\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,0,\,±\frac12\right).$$

Representations
A truncated octahedral prism has the following Coxeter diagrams:


 * x o4x3x (full symmetry)
 * x x3x3x (bases have A3 symmetry)
 * oo4xx3xx&#x (bases considered separately)
 * xx3xx3xx&#x (bases separately under A3)
 * xxxxx xuxux4ooqoo&#xt (BC2×A1 axial, cube-first)
 * xxxx xuxx3xxux&#xt (A2×A1 axial, hexagonal prism-first)