Small icosihemidodecahedron
| Small icosihemidodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 26, E = 60 V = 30 (χ = −4) |
| Faces by sides | 20{3}+6{10} |
| Coxeter diagram |     (double covering)
|
| 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 |
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
[edit]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
[edit]References
[edit]- ^ Maeder, Roman. "49: small icosihemidodecahedron". MathConsult.
External links
[edit]
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