Small dodecicosahedron
In geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U50. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.
| Small dodecicosahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 32, E = 120 V = 60 (χ = −28) |
| Faces by sides | 20{6}+12{10} |
| Coxeter diagram |     (with extra double-covered triangles)  (with extra double-covered pentagrams) |
| Wythoff symbol | 3 5 (3/2 5/4) | |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U50, C64, W90 |
| Dual polyhedron | Small dodecicosacron |
| Vertex figure |  6.10.6/5.10/9 |
| Bowers acronym | Siddy |
3D model of a small dodecicosahedron
Related polyhedra
It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small icosicosidodecahedron (having the hexagonal faces in common) and the small ditrigonal dodecicosidodecahedron (having the decagonal faces in common).
 Great stellated truncated dodecahedron |
 Small icosicosidodecahedron |
 Small ditrigonal dodecicosidodecahedron |
Small dodecicosahedron |
References
- Maeder, Roman. "50: small dodecicosahedron". MathConsult.
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