Small icosicosidodecahedron
Polyhedron
From Wikipedia, the free encyclopedia
In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U31. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices.[1]
| Small icosicosidodecahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 52, E = 120 V = 60 (χ = −8) |
| Faces by sides | 20{3}+12{5/2}+20{6} |
| Coxeter diagram |     |
| Wythoff symbol | 5/2 3 | 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U31, C40, W71 |
| Dual polyhedron | Small icosacronic hexecontahedron |
| Vertex figure |  6.5/2.6.3 |
| Bowers acronym | Siid |
Related polyhedra
It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small ditrigonal dodecicosidodecahedron (having the triangular and pentagrammic faces in common) and the small dodecicosahedron (having the hexagonal faces in common).
 Great stellated truncated dodecahedron |
Small icosicosidodecahedron |
 Small ditrigonal dodecicosidodecahedron |
 Small dodecicosahedron |
