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.

This polychoron can be alternated into an omnisnub 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:
 * (±1/2, ±1/2, ±(3+2$\sqrt{2}$)/2, ±1/2)
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(4+$\sqrt{10+2√5}$)/4, ±1/2)
 * (±1, ±(3+$\sqrt{2}$)/4, ±(7+3$\sqrt{8+3√5}$)/4, ±1/2)
 * (±(3+$\sqrt{5}$)/4, ±3(1+$\sqrt{3}$)/4, ±(3+$\sqrt{15}$)/2, ±1/2)
 * (±(1+$\sqrt{(5+√5)/10}$)/2, ±(5+3$\sqrt{(5+2√5)/15}$)/4, ±(5+$\sqrt{5}$)/4, ±1/2)

Representations
A great rhombicosidodecahedral prism has the following Coxeter diagrams:


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