Great rhombicosidodecahedral prism

The great rhombicosidodecahedral prism or griddip, is a prismatic uniform polychoron that consists of 2 great rhombicosidodecahedra, 12 decagonal prisms, 20 hexagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the great rhombicosidodecahedron. As such it is also a convex segmentochoron (designated K-4.150 on Richard Klitzing's list).

This polychoron can be alternated into a snub dodecahedral antiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a great 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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt5}{2},\,±\frac{4+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac12\right).$$

Representations
A great rhombicosidodecahedral prism has the following Coxeter diagrams:


 * x x5x3x (full symmetry)
 * xx5xx3xx&#x (bases considered separately)