Grand ditetrahedronary hexacosidishecatonicosachoron

The grand ditetrahedronary hexacosidishecatonicosachoron, or gadtaxady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 great icosidodecahedra. 4 great stellated dodecahedra, 4 tetrahedra, and 6 great icosidodecahedra join at each vertex, with a small rhombitetratetrahedron as the vertex figure.

The grand ditetrahedronary hexacosidishecatonicosachoron contains the vertices of a great dodecicosidodecahedral prism and decagrammic duoprism.

Vertex coordinates
The vertices of a grand ditetrahedronary hexacosidishecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of: together with all the even permutations of:
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,0,\,0\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12\right).$$

Related polychora
THe grand ditetrahedronary hexacosidishecatonicosachoron is the colonel of a regiment of 37 members, plus 5 fissaries and a compound, as well as a number of scaliform members.