Rectified great hecatonicosachoron

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

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

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

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

The rectified great hecatonicosachoron also has the same circumradius as the hexagonal-decagonal duoprism.

Uniform polychoron compounds composed of rectified great hecatonicosachora include:


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