Ditetrahedronary dishecatonicosachoron

The ditetrahedronary dishecatonicosachoron, or dattady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra and 120 small ditrigonary icosidodecahedra. 4 small ditrigonary icosidodecahedra and 4 great stellated dodecahedra join at each vertex, with a variant of the truncated tetrahedron as the vertex figure.

The ditetrahedronary dishecatonicosachoron contains the vertices and edges of a hexagonal duoprism, rhombidodecadodecahedral prism, and decachoron.

Vertex coordinates
The vertices of a ditetrahedronary dishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:
 * $$\left(±1,\,±1,\,0,\,0\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4}\right),$$

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

Related polychora
The ditetrahedronary dishecatonicosachoron is the colonel of a regiment with 37 members, plus four fissaries and two compounds, as well as a number of scaliform members.