Icosidodecatruncated icosidodecahedral prism

The icosidodecatruncated icosidodecahedral prism or idtiddip, is a prismatic uniform polychoron that consists of 2 icosidodecatruncated icosidodecahedra, 12 decagrammic prisms, 12 decagonal prisms, and 20 hexagonal prisms. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the icosidodecatruncated icosidodecahedron.

Vertex coordinates
The vertices of an icosidodecatruncated icosidodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac32,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right).$$