Rectified great faceted hexacosichoron

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

Vertex coordinates
The vertices of a rectified great faceted hexacosichoron of edge length 1 are given by all permutations of: along with even permutations of:
 * $$\left(0,\,0,\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-2}{2}\right).$$

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

Uniform polychoron compounds composed of rectified great faceted hexacosichora include:


 * Rectified great faceted chirotetrahedral dishexacosichoron (2)
 * Rectified great faceted snub pentishecatonicosachoron (5)
 * Rectified great faceted snub decahecatonicosachoron (10)