Small inverted retrosnub icosicosidodecahedron

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

Vertex coordinates
A small inverted retrosnub icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

$$\Biggl(0,\pm\frac{3-\sqrt{3+2\sqrt{5}}}{4},\pm\frac{\sqrt{5}-1+\sqrt{6\sqrt{5}-2}}{8}\Biggr)$$

$$\Biggl(\pm\frac{1}{2},\pm\frac{\sqrt{3+2\sqrt{5}}-\sqrt{5}}{4},\pm\frac{1-\sqrt{5}+\sqrt{6\sqrt{5}-2}}{8}\Biggr)$$

$$\Biggl(\pm\frac{\sqrt{5}-1}{4},\pm\frac{\sqrt{3+2\sqrt{5}-1}}{4},\pm\frac{3+\sqrt{5}-\sqrt{6\sqrt{5}-2}}{8}\Biggr)$$