| Small dodecahemidodecahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 18, E = 60V = 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. 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.
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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 |
External links
References
Maeder, Roman. "51: small dodecahemidodecahedron". MathConsult. https://www.mathconsult.ch/static/unipoly/51.html ↩