Quasitruncated dodecadodecahedral prism

The quasitruncated dodecadodecahedral prism or quitdiddip, is a prismatic uniform polychoron that consists of 2 quasitruncated dodecadodecahedra, 12 decagrammic prisms, 12 decagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the quasitruncated dodecadodecahedron.

The great rhombicosidodecahedral pirsm can be vertex-inscribed into the rectified small ditrigonary hexacosihecatonicosachoron.

Vertex coordinates
The vertices of a quasitruncated dodecadodecahedral 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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±1,\,±\frac12\right).$$.