Small icosicosidodecahedron
TypeUniform star polyhedron
ElementsF = 52, E = 120
V = 60 (χ = 8)
Faces by sides20{3}+12{5/2}+20{6}
Coxeter diagram
Wythoff symbol5/2 3 | 3
Symmetry groupIh, [5,3], *532
Index referencesU31, C40, W71
Dual polyhedronSmall icosacronic hexecontahedron
Vertex figure
6.5/2.6.3
Bowers acronymSiid
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]

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

References

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