Rectified small ditrigonary hexacosihecatonicosachoron

The rectified small ditrigonary hexacosihecatonicosachoron, or rissidtixhi, is a nonconvex uniform polychoron that consists of 600 regular octahedra, 120 small ditrigonary icosidodecahedra, and 120 great icosidodecahedra. 2 small ditrigonary icosidodecahedra, 3 great icosidodecahedra, and 3 octahedra join at each ditrigonal prismatic vertex. As the name suggests, it can be obtained by rectifying the small ditrigonary hexacosihecatonicosachoron.

Vertex coordinates
The vertices of a rectified small ditrigonary hexacosihecatonicosachoron of edge length 1 are given by all permutations of: along with all even permutations of:
 * $$\left(0,\,0,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(0,\,±1,\,±1,\,±1\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac32\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$


 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{4},\,±\frac32,\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{3+\sqrt5}{4},\,±1\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right).$$

Related polychora
The rectified small ditrigonary hexacosihecatonicosachoron is the colonel of the largest non-snub regiment of uniform polychora, containing a total of 157 members, plus three compounds and three fissaries. Jonathan Bowers divides the rissidtixhi regiment into twenty subcategories.

Rissidtixhi regiment