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Small dodecicosahedron

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Small dodecicosahedron
Type Uniform star polyhedron
Elements F = 32, E = 120
V = 60 (χ = −28)
Faces by sides 20{6}+12{10}
Coxeter diagram (with extra double-covered triangles)
(with extra double-covered pentagrams)
Wythoff symbol 3 5 (3/2 5/4) |
Symmetry group Ih, [5,3], *532
Index references U50, C64, W90
Dual polyhedron Small dodecicosacron
Vertex figure
6.10.6/5.10/9
Bowers acronym Siddy
3D model of a small dodecicosahedron

In geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U50. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.

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It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small icosicosidodecahedron (having the hexagonal faces in common) and the small ditrigonal dodecicosidodecahedron (having the decagonal faces in common).


Great stellated truncated dodecahedron

Small icosicosidodecahedron

Small ditrigonal dodecicosidodecahedron

Small dodecicosahedron

References

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  1. ^ Maeder, Roman. "50: small dodecicosahedron". MathConsult.
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