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
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
References
- ^ Maeder, Roman. "49: small icosihemidodecahedron". MathConsult.
External links
- Weisstein, Eric W. "Small icosihemidodecahedron". MathWorld.
- Uniform polyhedra and duals
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polyhedra (nonconvex
regular polyhedra)
of Kepler-Poinsot
polyhedra
hemipolyhedra
uniform polyhedra
- medial rhombic triacontahedron
- small stellapentakis dodecahedron
- medial deltoidal hexecontahedron
- small rhombidodecacron
- medial pentagonal hexecontahedron
- medial disdyakis triacontahedron
- great rhombic triacontahedron
- great stellapentakis dodecahedron
- great deltoidal hexecontahedron
- great disdyakis triacontahedron
- great pentagonal hexecontahedron
uniform polyhedra with
infinite stellations
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