Small icosicosidodecahedron

The small icosicosidodecahedron, or siid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 20 hexagons. One triangle, one pentagram, and two hexagons join at each vertex.

Vertex coordinates
A small icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
 * (±1/2, ±(1+$\sqrt{(17+3√5)/8}$)/4, ±($\sqrt{5}$–1)/2)
 * (0, ±(3+$\sqrt{3}$)/4, ±$\sqrt{5}$/2)
 * (±1/2, ±1, ±(3+$\sqrt{3}$)/4)

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