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:
 * (±(3–$\sqrt{5}$)/2, ±(3–$\sqrt{2}$)/2, 0, 0),
 * (±(3$\sqrt{10}$–5)/4, ±(3–$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/4),
 * (±($\sqrt{5}$–2)/2, ±($\sqrt{5}$–2)/2, ±($\sqrt{5}$–2)/2, ±1/2),
 * (±(7–3$\sqrt{5}$)/4, ±($\sqrt{5}$–1)/4, ±($\sqrt{5}$–1)/4, ±($\sqrt{5}$–1)/4),
 * (±(7–3$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/4, ±1/2, 0),
 * (±($\sqrt{5}$–2)/2, ±(3$\sqrt{5}$–5)/4, 0, ±($\sqrt{5}$–1)/4),
 * (±($\sqrt{5}$–2)/2, ±(3–$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/2, ±($\sqrt{5}$–1)/4).