Rhombicosahedron

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Rhombicosahedron
File:Rhombicosahedron.png
Type	Uniform star polyhedron
Elements	F = 50, E = 120 V = 60 (χ = −10)
Faces by sides	30{4}+20{6}
Coxeter diagram	Template:CDD (with extra double-covered pentagrams) Template:CDD (with extra double-covered pentagons)
Wythoff symbol
Symmetry group	I_h, [5,3], *532
Index references	U₅₆, C₇₂, W₉₆
Dual polyhedron	Rhombicosacron
Vertex figure	File:Rhombicosahedron vertfig.png 4.6.4/3.6/5
Bowers acronym	Ri

3D model of a rhombicosahedron

In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U₅₆. It has 50 faces (30 squares and 20 hexagons), 120 edges and 60 vertices.^[1] Its vertex figure is an antiparallelogram.

Related polyhedra

A rhombicosahedron shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the square faces in common) and the icosidodecadodecahedron (having the hexagonal faces in common).

File:Rhombidodecadodecahedron convex hull.png Convex hull	File:Rhombidodecadodecahedron.png Rhombidodecadodecahedron	File:Icosidodecadodecahedron.png Icosidodecadodecahedron
File:Rhombicosahedron.png Rhombicosahedron	File:UC32-10 triangular prisms.png Compound of ten triangular prisms	File:UC33-20 triangular prisms.png Compound of twenty triangular prisms

3D model of a rhombicosacron

The rhombicosacron is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U₅₆. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces.