Small inverted retrosnub icosicosidodecahedron

{{Infobox polytope }} 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.
 * dim = 3
 * img=Small retrosnub icosicosidodecahedron.png
 * 3d=Small retrosnub icosicosidodecahedron.stl
 * off = Small retrosnub icosicosidodecahedron.off
 * obsa = Sirsid
 * type=Uniform
 * coxeter = s5/2s3/2s3/2*a
 * symmetry = H3, order 120
 * army=Semi-uniform Tid
 * reg=Sirsid
 * faces = 60 triangles, 20 hexagrams, 12 pentagrams
 * edges = 60+60+60
 * vertices = 60
 * verf = Mirror-symmetric hexagon, edge lengths 1, 1, 1, 1, 1, ($\sqrt{5}$–1)/2
 * dual = Small hexagrammic hexecontahedron
 * circum=$$\frac{\sqrt{13+3\sqrt5-\sqrt{102+46\sqrt5}}}{4} ≈ 0.58069$$
 * volume = $$\frac{45+39\sqrt5-5\sqrt{302+150\sqrt5}}}{12} ≈ 0.49764$$
 * density = 38
 * euler=-8
 * dih=5/2–3: $$\arccos\left(\sqrt{\frac{15-2\sqrt5-2\sqrt{30\sqrt5-65}}{15}}\right) ≈ 44.45753°$$
 * dih2=3–3: $$\arccos\left(\frac{\sqrt{3+2\sqrt5}}{3}\right) ≈ 24.33196°$$
 * pieces = 3060
 * loc = 213
 * conj=Small snub icosicosidodecahedron
 * conv=No
 * orient=Yes
 * nat=Tame

In terms of level of complexity, this is the most complex uniform polyhedron.

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

Representations
A small inverted retrosnub icosicosidodecahedron has the following Coxeter diagrams:


 * s3/2s3/2s5/2*a
 * o5ß3/2ß (as holosnub)