Great dodecicosidodecahedral prism

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

The great dodecicosidodecahedral prism can be vertex-inscribed into the grand ditetrahedronary hexacosidishecatonicosachoron.

Vertex coordinates
The vertices of a great dodecicosidodecahedral 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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{4},\,±\frac12\right).$$