Quasitruncated great stellated hecatonicosachoron

The quasitruncated great stellated hecatonicosachoron, or quit gishi, is a nonconvex uniform polychoron that consists of 120 regular icosahedra and 120 quasitruncated great stellated dodecahedra. One icosahedron and five quasitruncated great stellated dodecahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the great stellated hecatonicosachoron.

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

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