Great snub dodecicosidodecahedron

The great snub dodecicosidodecahedron, or gisdid, is a uniform polyhedron. It consists of 60 snub triangles, 20 more triangles, and 24 pentagrams that fall in coplanar pairs of one prograde, one retrograde. Four triangles and two pentagrams meet at each vertex.

It is the only chiral uniform polyhedron with an achiral convex hull. As such, it cannot be made into a compound with its reflection. If the pentagrams are removed, however, the disnub icosahedron is formed.

This polyhedron's edges are a subset of those of the great dirhombicosidodecahedron, and it shares the same vertices.

Vertex coordinates
A great snub dodecicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\sqrt{\frac{\sqrt5-1-2\sqrt{\sqrt5-2}}{2}},\,±\sqrt{\frac{3-\sqrt5-\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2+\sqrt{2\sqrt5-2}}{8}}\right),$$
 * $$\left(0,\,±\frac{\sqrt{3-\sqrt5}}{2},\,±\frac{\sqrt{\sqrt5-1}}{2}\right),$$
 * $$\left(±\sqrt{\frac{3-\sqrt5+\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2-\sqrt{2\sqrt5-2}}{8}},\,±\sqrt{\frac{\sqrt5-1+2\sqrt{\sqrt5-2}}{8}}\right).$$