Great dodecicosidodecahedron

The great dodecicosidodecahedron, or gaddid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagrams. One triangle, one pentagram, and two decagrams join at each vertex.

Vertex coordinates
A great dodecicosidodecahedron of edge length 1 has vertex coordinates given by all permutations of along with all even permutations of
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{4}\right).$$

Related polyhedra
The great dodecicosidodecahedron is the colonel of a three-member regiment that also includes the quasirhombicosidodecahedron and the great rhombidodecahedron.