Rectified great stellated hecatonicosachoron

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

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

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