Great ditrigonal hecatonicosiprismatodishecatonicosachoron

The great ditrigonal hecatonicosiprismatodishecatonicosachoron, or gid thipady, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated dodecahedra, 120 great ditrigonal dodecicosidodecahedra, and 120 quasitruncated dodecadodecahedra. 1 pentagonal prism, 1 truncated dodecahedron, 1 great ditrigonal dodecicosidodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.

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

Related polychora
The great ditrigonal hecatonicosiprismatodishecatonicosachoron is the colonel of a 3-member regiment that also includes the great hecatonicosiprismatodishecatonicosachoron and great hecatonicosihecatonicosihecatonicosachoron.