Truncated great hecatonicosachoron

The truncated great hecatonicosachoron, or tighi, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 120 truncated great dodecahedra. One small stellated dodecahedron and five truncated great dodecahedra join at each vertex. As the name suggests, it can be obtained by truncating the great hecatonicosachoron.

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

Related polychora
The truncated great hecatonicosachoron is the colonel of a two-member regiment that also includes the truncated grand hecatonicosachoron.