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:
 * $$\left(±\frac{\sqrt5}{2},\,±\frac12,\,±\frac12,\,±\frac12\right)$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12\right).$$