Prismatodishecatonicosachoron

The prismatodishecatonicosachoron, or padohi, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 small stellated dodecahedra, 1200 triangular prisms, and 720 pentagrammic prisms. 1 icosahedron, 1 small stellated dodecahedron, 5 triangular prisms, and 5 pentagrammic prisms join at each vertex. It is the result of expanding the cells of either a small stellated hecatonicosachoron or a faceted hexacosichoron outwards.

The prismatodishecatonicosachoron contains the vertices of a prismatorhombisnub icositetrachoron.

Blending 10 prismatodishecatonicosachora results in the small difusiprismatosnub diprismatosnub disdishexacosichoron, which is scaliform.

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

Related polychora
The prismatodishecatonicosachoron is the colonel of a regiment that includes 81 uniform members, as well as 78 fissary uniforms, 18 normal and 59 fissary scaliforms, and 1 scaliform compound.