Rhombidodecadodecahedral prism

The rhombidodecadodecahedral prism or radiddip is a prismatic uniform polychoron that consists of 2 rhombidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 30 cubes. Each vertex joins 1 rhombidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 cubes. As the name suggests, it is a prism based on the rhombidodecadodecahedron.

The rhombidodecadodecahedral prism can be vertex-inscribed into the ditetrahedronary dishecatonicosachoron.

Vertex coordinates
The vertices of a rhombidodecadodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of: along with all even permutations of the first three coordinates of:
 * (±$\sqrt{5}$/2, ±1/2, ±1/2, ±1/2)
 * (0, ±(3+$\sqrt{2}$)/4, ±(3–$\sqrt{5}$)/4, ±1/2)
 * (±1, ±($\sqrt{2}$–1)/4, ±(1+$\sqrt{2}$)/4, ±1/2)