Small icosicosidodecahedron

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

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]

3D model of a small icosicosidodecahedron

Related polyhedraEdit

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 alsoEdit


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

External linksEdit