Small blendic disprismatodishecatonicosachoron

The small blendic disprismatodishecatonicosachoron, or sabbadipady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra, 720 pentagonal prisms, and 720 pentagrammic prisms. 1 great stellated dodecahedron, 3 pentagonal prisms, 3 pentagrammic prisms, and 3 quasitruncated small stellated dodecahedra join at each vertex.

It contains the vertices and edges of a truncated great grand hecatonicosachoron, quasitruncated small stellated hecatonicosachoron, and small disprismatodishecatonicosachoron, which each use all of its vertices. It can also be constructed as the blend of the latter two, with the common dodecahedral cells blending out.

Vertex coordinates
The vertices of a small blendic disprismatodishecatonicosachoron of edge length 1 are all permutations of:

along with the even permutations of:
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\,±\frac{1+|sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±1\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{3\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac32,\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right).$$

Related polychora
The small blendic disprismatodishecatonicosachoron is the colonel of a regiment that includes 12 uniform members, along with 4 fissaries and 3 mixed compounds.