Great ditrigonal dodecicosidodecahedral prism

The great ditrigonal dodecicosidodecahedral prism or gidditdiddip is a prismatic uniform polychoron that consists of 2 great ditrigonal dodecicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 12 decagrammic prisms. Each vertex joins 1 great ditrigonal dodecicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great ditrigonal dodecicosidodecahedron.

Vertex coordinates
The vertices of a great ditrigonal dodecicosidodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±1,\,±\frac{3-\sqrt5}{4},\,±\frac12\right).$$