Rectified great grand stellated hecatonicosachoron

The rectified great grand stellated hecatonicosachoron, or rigogishi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 great icosidodecahedra. Two tetrahedra and three great icosidodecahedra join at each triangular prismatic vertex. As the name suggests, it can be obtained by rectifying the great grand stellated hecatonicosachoron.

Vertex coordinates
The vertices of a rectified great grand stellated hecatonicosachoron of edge length 1 are given by all permutations of: along with all even permutations of:
 * $$\left(0,\,0,\,±\frac{\sqrt5-1}{2},\,±\left(\sqrt5-2\right)\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7-3\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\left(\sqrt5-2\right),\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right).$$