Small dodecicosidodecahedron
From Infogalactic: the planetary knowledge core
Small dodecicosidodecahedron | |
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Type | Uniform star polyhedron |
Elements | F = 44, E = 120 V = 60 (χ = −16) |
Faces by sides | 20{3}+12{5}+12{10} |
Wythoff symbol | 3/2 5 | 5 3 5/4 | 5 |
Symmetry group | Ih, [5,3], *532 |
Index references | U33, C42, W72 |
Dual polyhedron | Small dodecacronic hexecontahedron |
Vertex figure | 5.10.3/2.10 |
Bowers acronym | Saddid |
In geometry, the small dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U33. Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the triangular and pentagonal faces in common), and with the small rhombidodecahedron (having the decagonal faces in common).
Rhombicosidodecahedron |
Small dodecicosidodecahedron |
Small rhombidodecahedron |
Small stellated truncated dodecahedron |
Compound of six pentagrammic prisms |
Compound of twelve pentagrammic prisms |
Dual
Small dodecacronic hexecontahedron | |
---|---|
Type | Star polyhedron |
Face | |
Elements | F = 60, E = 120 V = 44 (χ = −16) |
Symmetry group | Ih, [5,3], *532 |
Index references | DU33 |
dual polyhedron | Small dodecicosidodecahedron |
The dual polyhedron to the small dodecicosidodecahedron is the small dodecacronic hexecontahedron. It is visually identical to the small rhombidodecacron.
References
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External links
- Weisstein, Eric W., "Uniform Polyhedron", MathWorld.
- Weisstein, Eric W., "Small dodecicosidodecahedron", MathWorld.
- Weisstein, Eric W., "Small dodecacronic hexecontahedron", MathWorld.
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