Small_dodecicosahedron Knowpia

Small dodecicosahedron

Type	Uniform star polyhedron
Elements	F = 32, E = 120 V = 60 (χ = −28)
Faces by sides	20{6}+12{10}
Coxeter diagram	(with extra double-covered triangles) (with extra double-covered pentagrams)
Wythoff symbol	3 5 (3/2 5/4) \|
Symmetry group	I_h, [5,3], *532
Index references	U₅₀, C₆₄, W₉₀
Dual polyhedron	Small dodecicosacron
Vertex figure	6.10.6/5.10/9
Bowers acronym	Siddy

In geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U₅₀. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices.^[1] Its vertex figure is a crossed quadrilateral.

Related polyhedra edit

It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small icosicosidodecahedron (having the hexagonal faces in common) and the small ditrigonal dodecicosidodecahedron (having the decagonal faces in common).