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.

A semi-uniform variant of this polyhedron can be constructed as a rectified small ditrigonary icosidodecahedron.

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

Representations
A small icosicosidodecahedron has the following Coxeter diagrams:


 * x5/2o3x3*a
 * ß5o3x (as holosnub)

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