Small icosihemidodecahedron
From HandWiki
Short description: Uniform star polyhedron with 26 faces
| Small icosihemidodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 26, E = 60 V = 30 (χ = −4) |
| Faces by sides | 20{3}+6{10} |
| Wythoff symbol | 3/2 3 | 5 (double covering) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U49, C63, W89 |
| Dual polyhedron | Small icosihemidodecacron |
| Vertex figure |  3.10.3/2.10 |
| Bowers acronym | Seihid |
File:Small icosihemidodecahedron.stl
In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral. It is a hemipolyhedron with its six decagonal faces passing through the model center.
It is given a Wythoff symbol, 3⁄2 3 | 5, but that construction represents a double covering of this model.
Related polyhedra
It shares its edge arrangement with the icosidodecahedron (its convex hull, having the triangular faces in common), and with the small dodecahemidodecahedron (having the decagonal faces in common).
 Icosidodecahedron |
Small icosihemidodecahedron |
 Small dodecahemidodecahedron |
See also
- Pentakis icosidodecahedron
- List of uniform polyhedra
References
External links
- Weisstein, Eric W.. "Small icosihemidodecahedron". http://mathworld.wolfram.com/SmallIcosihemidodecahedron.html.
- Uniform polyhedra and duals
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