Great ditrigonal dodecicosidodecahedron

The great ditrigonal dodecicosidodecahedron, or gidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagrams. One triangle, one pentagon, and two decagrams join at each vertex.

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

Related polyhedra
The great ditrigonal dodecicosidodecahedron is the colonel of a three-member regiment that also includes the great icosicosidodecahedron and the great dodecicosahedron.