Small icosicosidodecahedron

Small icosicosidodecahedron
File: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}
Coxeter diagram	Template:CDD
Wythoff symbol	3
Symmetry group	I_h, [5,3], *532
Index references	U₃₁, C₄₀, W₇₁
Dual polyhedron	Small icosacronic hexecontahedron
Vertex figure	File:Small icosicosidodecahedron vertfig.png 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]

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).

File:Great stellated truncated dodecahedron.png Great stellated truncated dodecahedron	File:Small icosicosidodecahedron.png Small icosicosidodecahedron	File:Small ditrigonal dodecicosidodecahedron.png Small ditrigonal dodecicosidodecahedron	File:Small dodecicosahedron.png Small dodecicosahedron