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:
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,±\frac12\right).$$

Representations
A cuboctahedral prism has the following Coxeter diagrams:


 * x o4x3o (full symmetry)
 * x x3o3x (rhombitetratetrahedral prism)
 * s2s4x3o (bases as rhombitetratetrahedra)
 * 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)

Related polychora
A cuboctahedral prism can be cut in half to produce two triangular cupolic prisms with the base triangular prisms in rotated orientations.

The regiment of the cuboctahedral prism also includes the octahemioctahedral prism and the cubohemioctahedral prism.