Cuboctahedral prism

The cuboctahedral prism or cope is a prismatic uniform polychoron that consists of 2 cuboctahedra, 6 cubes and 8 triangular prisms. Each vertex joins 1 cuboctahedron, 2 cubes, and 2 triangular prisms. As the name suggests, it is a prism based on the cuboctahedron. As such it is also a convex segmentochoron (deisngated K-4.43 on Richard Klitzing's list).

Vertex coordinates
The vertices of a cuboctahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:
 * (±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0, ±1/2)

Representations
A cuboctahedral prism has the following Coxeter diagrams:


 * x o4x3o (full symmetry)
 * x x3o3x (rhombitetratetrahedral prism)
 * oo4xx3oo&#x (bases considered separately)
 * xx3oo3xx&#x (rhombitetratetrahedral bases considered separately)
 * xxx xox4oqo&#xt (BC2×A1 axial, cube-first)
 * xxx xxo3oxx&#xt (A2×A1 axial, triangular prism-first)
 * xxx qqo qoq oqq&#zx (A1×A1×A1×A1 symmetry)