Rectified great stellated hecatonicosachoron

The rectified great stellated hecatonicosachoron, or ragishi, is a nonconvex uniform polychoron that consists of 120 icosahedra and 120 great icosidodecahedra. Two icosahedra and five great icosidodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great stellated hecatonicosachoron.

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

along with even permutations of:
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±1,\,±\frac{3-\sqrt5}{4}\right).$$

Related polychora
The rectified great stellated hecatonicosachoron is the colonel of a regiment with 15 members. Of these, one other besides the colonel itself is Wythoffian (the rectified grand stellated hecatonicosachoron), two are hemi-Wythoffian (the small pentagrammal antiprismatoverted dishecatonicosachoron and pentagonal retroprismatoverted hexacosihecatonicosachoron), and one is noble (the great retropental hecatonicosachoron).

It has the same circumradius as the hexagonal-decagrammic duoprism.

Uniform polychoron compounds composed of great stellated hecatonicosachora include:


 * Rectified great stellated diacositetracontachoron (2)
 * Rectiied great stellated chirohexacosichoron (5)
 * Rectified great stellated dishexacosichoron (10)