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 of a hexagonal duoprism, rhombidodecadodecahedral prism, and the decachoron.

Vertex coordinates
The vertices of a ditetrahedronary dishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of: together with all the even permutations of:
 * (±1, ±1, 0, 0),
 * (±$\sqrt{5}$/2, ±1/2, ±1/2, ±1/2),
 * (±(1+$\sqrt{2}$)/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/4),
 * (±(3+$\sqrt{5}$)/4, ±($\sqrt{5}$–1)/4, ±($\sqrt{5}$–1)/4, ±($\sqrt{5}$–1)/4),
 * (±(3+$\sqrt{5}$)/4, ±1/2, ±(3–$\sqrt{5}$)/4, 0),
 * (±(1+$\sqrt{5}$)/4, ±$\sqrt{5}$/2, 0, ±($\sqrt{5}$–1)/4),
 * (±(1+$\sqrt{5}$)/4, ±1/2, ±1, ±($\sqrt{5}$–1)/4).