Great rhombicosidodecahedral prism

The great rhombicosidodecahedral prism or griddip is one of the uniform polychora made as the prism product of a uniform polyhedron and a dyad that consists of 2 great rhombicosidodecahedra, 12 decagonal prisms, 20 hexagonal prisms and 30 cubes.

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 and sign changes of the first three coordinates of: along with all even permutations and all sign changes of the first three coordinates of:
 * (1/2, (1+$\sqrt{2}$)/2, (1+2$\sqrt{3}$)/2, ±1/2)
 * (±1/2, ±(2+$\sqrt{10+2√5}$)/2, ±(4+$\sqrt{2}$)/4, ±1/2)
 * (±1, ±(3+$\sqrt{8+3√5}$)/4, ±(7+3$\sqrt{2}$)/4, ±1/2)
 * (±(3+$\sqrt{2}$)/4, ±3(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2, ±1/2)
 * (±(1+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, ±1/2)