Small dodecahemidodecahedron
| 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, [5,3], *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.[1] 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
[edit]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
[edit]- ^ Maeder, Roman. "51: small dodecahemidodecahedron". MathConsult.
External links
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