Small snub icosicosidodecahedron

The small snub icosicosidodecahedron, or seside, is a uniform polyhedron. It consists of 60 snub triangles, 40 more triangles that create 20 hexagrams due to pairs falling in the same plane, and 12 pentagrams. Five triangles and one pentagram meet at each vertex.

It can be obtained as a holosnub truncated icosahedron, after adjusting all edge lengths to be equal.

Vertex coordinates
A small snub icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(0,\,±\frac{3+\sqrt{3+2\sqrt5}}{4},\,±\frac{1-\sqrt5+\sqrt{6\sqrt5-2}}{8}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5+\sqrt{3+2\sqrt5}}{4},\,±\frac{\sqrt5-1+\sqrt{6\sqrt5-2}}{8}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt{3+2\sqrt5}}{4},\,±\frac{3+\sqrt5+\sqrt{6\sqrt5-2}}{8}\right).$$

Representations
A small snub icosicosidodecahedron has the following Coxeter diagrams:


 * s5/2s3s3*a
 * o5ß3ß (as holosnub)