Great sphenoverted trishecatonicosachoron

The great sphenoverted trishecatonicosachoron, or gwavathi, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 dodecadodecahedra, and 120 great dodecicosidodecahedra. 1 dodecadodecahedron, 2 quasitruncated small stellated dodecahedra, and 2 great dodecicosidodecahedra join at each vertex.

Vertex coordinates
Coordinates for the vertices of a great sphenoverted trishecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±1,\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-2}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±(\sqrt5-2),\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{3-\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{\sqrt5-2}{2}\right).$$

Related polychora
The great sphenoverted trishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the quasirhombated great faceted hexacosichoron, rhombic great hecatonicosihecatonicosachoron, great pseudorhombic hecatonicosihecatonicosachoron, grand quasirhombic dishecatonicosachoron, great prismatohecatonicosintercepted dishecatonicosachoron, and grand hecatonicosintercepted trishecatonicosachoron.