Great rhombicuboctahedral prism

The great rhombicuboctahedral prism, or gircope, is a prismatic uniform polychoron that consists of 2 great rhombicuboctahedra, 6 octagonal prisms, 8 hexagonal prisms, and 12 cubes. Each vertex joins one of each type of cell. As the name suggests, it is a prism based on the great rhombicuboctahedron. As such it is also a convex segmentochoron (designated K-4.125 on Richard Klitzing's list).

The great rhombicuboctahedral prism can be obtained as the central segment of the prismatorhombated tesseract in small rhombicuboctahedron-first orientation.

This polychoron can be alternated into a snub cubic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pyritosnub alterprism, which is also nonuniform.

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

Representations
The great rhombicuboctahedral prism has the following Coxeter diagrams:


 * x x4x3x (full symmetry)
 * xx4xx3xx&#x (bases considered separately)
 * xxxxxx xuxxux4xxwwxx&#xt (BC2×A1 symmetry, octagonal prism-first)