| Small dodecahemidodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 18, E = 60 V = 30 (χ = −12) |
| Faces by sides | 12{5}+6{10} |
| Coxeter diagram |     (double covering)
|
| Wythoff symbol | 5/4 5 | 5 (double covering) |
| Symmetry group | Ih, , *532 |
| Index references | U51, C65, W91 |
| Dual polyhedron | Small dodecahemidodecacron |
| Vertex figure |  5.10.5/4.10 |
| Bowers acronym | Sidhid |
In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U51. It has 18 faces (12 pentagons and 6 decagons), 60 edges, and 30 vertices. Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.
It is a hemipolyhedron with six decagonal faces passing through the model center.
Related polyhedra
It shares its edge arrangement with the icosidodecahedron (its convex hull, having the pentagonal faces in common), and with the small icosihemidodecahedron (having the decagonal faces in common).
 Icosidodecahedron |
 Small icosihemidodecahedron |
Small dodecahemidodecahedron |
References
- Maeder, Roman. "51: small dodecahemidodecahedron". MathConsult.
External links
| Star-polyhedra navigator | |
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| Kepler-Poinsot polyhedra (nonconvex regular polyhedra) | |
| Uniform truncations of Kepler-Poinsot polyhedra | |
| Nonconvex uniform hemipolyhedra | |
| Duals of nonconvex uniform polyhedra |
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| Duals of nonconvex uniform polyhedra with infinite stellations | |
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