Small disprismatodishecatonicosachoron

The small disprismatodishecatonicosachoron, or siddapady, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra, 120 great stellated dodecahedra, 720 pentagonal prisms, and 720 pentagrammic prisms. 1 dodecahedron, 1 great stellated dodecahedron, 3 pentagonal prisms, and 3 pentagrammic prisms join at each vertex. It is the result of expanding the cells of either a grand hecatonicosachoron or a great stellated hecatonicosachoron outwards.

Vertex coordinates
The vertices of a small disprismatodishecatonicosachoron of edge length 1 are all permutations of:

along with the even permutations of:
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\,±\frac{1+|sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±1\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{3\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac32,\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right).$$

Related polychora
The small disprismatodishecatonicosachoron is the colonel of a regiment of 7 members. The other members include the hecatonicosafaceted prismatodishecatonicosachoron, medial hecatonicosafaceted prismatodishecatonicosachoron, trishecatonicosachoron, disprismatohecatonicosachoron, small spinoprismatohecatonicosihecatonicosachoron, and great spinoprismatohecatonicosihecatonicosachoron.