Rectified great hecatonicosachoron

The rectified great hecatonicosachoron, or righi, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 120 dodecadodecahedra. Two small stellated dodecahedra and five dodecadodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great hecatonicosachoron.

Vertex coordinates
The vertices of a rectified great hecatonicosachoron of edge length 1 are given by all permutations of:
 * $$\left(0,\,0,\,±1,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$

along with even permutations of:
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±1,\,±\frac{3+\sqrt5}{4}\right).$$