Great grand stellated hecatonicosachoron

{{Infobox polytope 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.
 * type=Regular
 * dim = 4
 * img = Gogishi.png
 * off = Gogishi.off
 * obsa = Gogishi
 * cells = 120 great stellated dodecahedra
 * faces = 720 pentagrams
 * edges = 1200
 * vertices = 600
 * verf = Tetrahedron, edge length ($\sqrt{5}$–1)/2
 * schlafli = {5/2,3,3}
 * coxeter = x5/2o3o3o
 * army=Hi
 * reg=Gogishi
 * symmetry = H4, order 14400
 * circum = $$\frac{3\sqrt2-\sqrt{10}}{}2} ≈ 0.54018$$
 * rad1 = $$\frac{\sqrt{15}-2\sqrt3}{2} ≈ 0.20444$$
 * rad2 = $$\sqrt{\frac{65-29\sqrt5}{10}} ≈ 0.12411$$
 * inrad = $$\frac{7-3\sqrt5}{4} ≈ 0.072949$$
 * density = 191
 * euler=0
 * hypervolume = $$15\frac{47\sqrt5-105}{4} ≈ 0.35698$$
 * dich=72°
 * pieces = 9600
 * loc = 30
 * dual=Grand hexacosichoron
 * conjugate=Hecatonicosachoron
 * conv = No
 * orientable=Yes
 * nat=Tame}}

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:
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2},\,0,\,0\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1]{4},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac12,\,0\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-5}{4},\,0,\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5-1}{4}\right).$$