Great dipentary trishecatonicosachoron

The great dipentary trishecatonicosachoron, or gidipthi, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 small stellated dodecahedra, and 120 great dodecicosidodecahedra. 1 icosahedron, 1 small stellated dodecahedron, and 5 great dodecicosidodecahedra join at each vertex.

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

Related polychora
The great dipentary trishecatonicosachoron is the colonel of a regiment that includes 81 uniform members, as well as 78 fissary uniforms and a number of subsymmetric scaliforms.