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:
 * (±1/2, ±1/2, ±($\sqrt{(5–√5)/2}$–2)/2, ±1/2)
 * (0, ±(3–$\sqrt{5}$)/4, ±(5–$\sqrt{(5–√5)/2}$)/4, ±1/2)
 * (±($\sqrt{2}$–1)/4, ±($\sqrt{10}$–1)/2, ±(3–$\sqrt{2}$)/4, ±1/2)