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]

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

Related polyhedra

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

• List of uniform polyhedra