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Small icosicosidodecahedron

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Small icosicosidodecahedron
Type Uniform star polyhedron
Elements F = 52, E = 120
V = 60 (χ = −8)
Faces by sides 20{3}+12{5/2}+20{6}
Coxeter diagram
Wythoff symbol 5/2 3 | 3
Symmetry group Ih, [5,3], *532
Index references U31, C40, W71
Dual polyhedron Small icosacronic hexecontahedron
Vertex figure
6.5/2.6.3
Bowers acronym Siid
3D model of a small icosicosidodecahedron

In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U31. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices.[1]

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


Great stellated truncated dodecahedron

Small icosicosidodecahedron

Small ditrigonal dodecicosidodecahedron

Small dodecicosahedron

See also

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References

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  1. ^ Maeder, Roman. "31: small icosicosidodecahedron". MathConsult.
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