Small rhombicosidodecahedral prism

The small rhombicosidodecahedral prism or sriddip is a prismatic uniform polychoron that consists of 2 small rhombicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 30 cubes. Each vertex joins 1 small rhombicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 cubes. As the name suggests, it is a prism based on the small rhombicosidodecahedron. As such it is also a convex segmentochoron (designated K-4.111 on Richard Klitzing's list).

The small rhombicosidodecahedral prism can be vertex-inscribed into the small ditetrahedronary hexacosihecatonicosachoron.

Vertex coordinates
The vertices of a small rhombicosidodecahedral 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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\frac12\right).$$

Representations
The small rhombicosidodecahedral prism has the following Coxeter diagrams:


 * x x5o3x (full symmetry)
 * xx5oo3xx&#x (bases considered separately)

Related polychora
The pentagonal cupolic prism is a segmentochoron that can be obtained as a cap of the small rhombicosidodecahedral prism.

The regiment of the small rhombicosidodecahedral prism also includes the small dodecicosidodecahedral prism and the small rhombidodecahedral prism.