Great dirhombicosidodecahedral prism

The great dirhombicosidodecahedral prism or gidriddip is a prismatic uniform polychoron that consists of 2 great dirhombicosidodecahedra, 24 pentagrammic prisms, 40 triangular prisms, and 60 cubes (the latter three of these form pairs in the same hyperplane). Each vertex joins 1 great dirhombicosidodecahedron, 2 pentagrammic prisms, 2 triangular prisms, and 4 cubes. As the name suggests, it is a prism based on the great dirhombicosidodecahedron.

Vertex coordinates
A great dirhombicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of the first three coordinates of:
 * $$\left(±\sqrt{\frac{\sqrt5-1-2\sqrt{\sqrt5-2}}{8}},\,±\sqrt{\frac{3-\sqrt5-\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2+\sqrt{2\sqrt5-2}}{8}},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt{3-\sqrt5}}{2},\,±\frac{\sqrt{\sqrt5-1}}{2},\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{3-\sqrt5+\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2-\sqrt{2\sqrt5-2}}{8}},\,±\sqrt{\frac{\sqrt5-1+2\sqrt{\sqrt5-2}}{8}},\,±\frac12\right).$$