Quasitruncated great grand stellated hecatonicosachoron

The quasitruncated great grand stellated hecatonicosachoron, or quit gogishi, is a convex uniform polychoron that consists of 600 regular tetrahedra and 120 quasitruncated great stellated dodecahedra. 1 tetrahedron and three quasitruncated great stellated dodecahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the great grand stellated hecatonicosachoron.

Vertex coordinates
The vertices of a truncated hecatonicosachoron of edge length 1 are given by all permutations of: along with all even permutations of:
 * $$\left(±\frac12,\,±\frac{5-2\sqrt5}2,\,±\frac{5-2\sqrt5}2,\,±\frac{5-2\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt5-2}2,\,±\frac{\sqrt5-2}2,\,±\frac{\sqrt5-2}2,\,±\frac{8-3\sqrt5}2\right),$$
 * $$\left(±\frac{3-\sqrt5}2,\,±\frac{3-\sqrt5}2,\,±\frac{3-\sqrt5}2,\,±\frac{7-3\sqrt5}2\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{13-5\sqrt5}2,\,±\frac{5\sqrt5-11}2\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7\sqrt5-15}4,\,±\frac{3\sqrt5-5}4\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}4,\,±3\frac{\sqrt5-2}2,\,±\frac{5\sqrt5-9}4\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}4,\,±\frac{8-3\sqrt5}2,\,±\frac{7-3\sqrt5}4\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}2,\,±\frac{7-3\sqrt5}2,\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}4,\,±\frac{7\sqrt5-15}4,\,±\frac{3-\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}2,\,±3\frac{\sqrt5-2}2,\,±\frac{5-2\sqrt5}2\right),$$
 * $$\left(±\frac{3-\sqrt5}4,\,±\frac{\sqrt5-1}2,\,±\frac{7\sqrt5-15}4,\,±\frac{\sqrt5-2}2\right),$$
 * $$\left(±\frac{3-\sqrt5}4,\,±\frac{3-\sqrt5}2,\,±\frac{13-5\sqrt5}2,\,±\frac{5-2\sqrt5}2\right),$$
 * $$\left(±\frac{3-\sqrt5}4,\,±(\sqrt5-2),\,±\frac{5\sqrt5-9}4,\,±\frac{5-2\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt5-1}2,\,±\frac{7-3\sqrt5}4,\,±\frac{5\sqrt5-11}2,\,±\frac{5-2\sqrt5}2\right),$$
 * $$\left(±\frac{\sqrt5-2}2,\,±\frac{3-\sqrt5}2,\,±\frac{5\sqrt5-11}2,\,±\frac{5\sqrt5-9}4\right),$$
 * $$\left(±\frac{\sqrt5-2}2,\,±\frac{3\sqrt5-5}4,\,±\frac{13-5\sqrt5}2,\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{3-\sqrt5}2,\,±\frac{3\sqrt5-5}4,\,±3\frac{\sqrt5-2}2,\,±\frac{7-3\sqrt5}4\right).$$