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 prismss 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 an omnisnub cubic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create an edge-snub octahedral hosochoron, 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:
 * (±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±1/2).

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)