Sphenoverted trishecatonicosachoron

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

Vertex coordinates
Coordinates for the vertices of a sphenoverted trishecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±1,\,±1,\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac32,\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±1,\,±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±1,\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±1,\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac32\right),$$
 * $$\left(±1,\,±\frac{\sqrt5}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right).$$

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