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.

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:
 * (±($\sqrt{5}$–1)/2, ±($\sqrt{10}$–1)/2, 0, 0),
 * (±(5–$\sqrt{2}$)/4, ±($\sqrt{5}$–1)/4, ±($\sqrt{7+3√5}$–1)/4, ±($\sqrt{5}$–1)/4),
 * (±(3–$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/4, ±(3–$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4),
 * (±($\sqrt{5}$–2)/2, ±1/2, ±1/2, ±1/2),
 * (±($\sqrt{5}$–2)/2, ±($\sqrt{5}$–1)/4, ±(1+$\sqrt{5}$)/4, 0),
 * (±(3–$\sqrt{5}$)/4, ±(5–$\sqrt{5}$)/4, 0, ±1/2),
 * (±(3–$\sqrt{5}$)/4, ±($\sqrt{5}$–1)/4, ±($\sqrt{5}$–1)/2, ±1/2).