Small icosicosidodecahedron

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	I_h, [5,3], *532
Index references	U₃₁, C₄₀, W₇₁
Dual polyhedron	Small icosacronic hexecontahedron
Vertex figure	6.5/2.6.3
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]

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).