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
 * (±($\sqrt{11–4√5}$–2)/2, ±1/2, ±1/2),
 * (0, ±(3–$\sqrt{5}$)/4, ±(5–$\sqrt{(5–√5)/2}$)/4),
 * (±($\sqrt{5}$–1)/4, ±($\sqrt{(5–√5)/2}$–1)/2, ±(3–$\sqrt{(5–2√5)/15}$)/4).

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