Great sphenoverted ditrigonal trishecatonicosachoron

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

Vertex coordinates
Coordinates for the vertices of a great sphenoverted ditrigonal trishecatonicosachoron of edge length 1 are given by all permutations of: together with all even permutations of:
 * $$\left(0,\,0,\,±(\sqrt5-1),\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-2}{2},\,±\frac{5+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac{3\sqrt5-5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{5-\sqrt5}{4},\,±\frac32,\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2},\,±\frac32,\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{9-\sqrt5}{4},\,±1\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±{3-\sqrt5}{2},\,±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±1\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±1,\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{9-\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±(\sqrt5-1),\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±3\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4},\,±1\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac32\right).$$

Related polychora
The great sphenoverted ditrigonal trishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the great retrosphenoverted hexacosidishecatonicosachoron, great hexacosidishecatonicosachoron, great retrohecatonicosihexacosihecatonicosachoron, great great dishecatonicosachoron, hexacosihecatonicosintercepted ditrigonal dishecatonicosachoron, and medial hecatonicosintercepted trishecatonicosachoron.