Great grand stellated hecatonicosachoron

The great grand stellated hecatonicosachoron, or gogishi, also commonly called the great grand stellated 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great stellated dodecahedra as cells, joining 3 to an edge and 4 to a vertex.

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