Medial prismatotrishecatonicosachoron

The medial prismatotrishecatonicosachoron, or mipthi, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 truncated dodecahedra, 120 great dodecicosidodecahedra, and 120 quasitruncated dodecadodecahedra. 1 pentagrammic prism, 1 truncated dodecahedron, 1 great dodecicosidodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.

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

Related polychora
The medial prismatotrishecatonicosachoron is the colonel of a three-member ergiment that also includes the prismatoquasirhombated great stellated hecatonicosachoron and the medial rhombiprismic hecatonicosihecatonicosachoron.