Rectified great grand hecatonicosachoron

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

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