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.

This polychoron can blend with quit sishi or tigaghi to form sabbadipady and gabbadipady respectively.