Rectified small stellated hecatonicosachoron

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

Vertex coordinates
The vertices of a rectified small stellated hecatonicosachoron of edge length 1 are given by all permutations of: along with all even permutations of:
 * $$\left(0,\,0,\,±1,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±3\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{2+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{2+\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right).$$