Small dodecahemicosahedron
In geometry, the small dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U62. It has 22 faces (12 pentagrams and 10 hexagons), 60 edges, and 30 vertices.[1] Its vertex figure is a crossed quadrilateral.
| Small dodecahemicosahedron | |
|---|---|
 | |
| Type | Uniform star polyhedron |
| Elements | F = 22, E = 60 V = 30 (χ = −8) |
| Faces by sides | 12{5/2}+10{6} |
| Wythoff symbol | 5/3 5/2 | 3 (double covering) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U62, C78, W100 |
| Dual polyhedron | Small dodecahemicosacron |
| Vertex figure |  6.5/2.6.5/3 |
| Bowers acronym | Sidhei |
3D model of a small dodecahemicosahedron
It is a hemipolyhedron with ten hexagonal faces passing through the model center.
Related polyhedra
Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the dodecadodecahedron (having the pentagrammic faces in common), and with the great dodecahemicosahedron (having the hexagonal faces in common).
 Dodecadodecahedron |
Small dodecahemicosahedron |
 Great dodecahemicosahedron |
 Icosidodecahedron (convex hull) |
Gallery
Traditional filling |
 Modulo-2 filling |
References
- Maeder, Roman. "62: small dodecahemicosahedron". MathConsult.
See also
External links
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