Rhombicosahedron

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Rhombicosahedron

Type	Uniform star polyhedron
Elements	F = 50, E = 120 V = 60 (χ = −10)
Faces by sides	30{4}+20{6}
Wythoff symbol(s)	2 3 (⁵/₄ ⁵/₂) \|
Symmetry group	I_h, [5,3], *532
Index references	U₅₆, C₇₂, W₉₆
Bowers acronym	Ri
4.6.⁴/₃.⁶/₅ (Vertex figure)	Rhombicosacron (dual polyhedron)

In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U₅₆. 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).

convex hull	Rhombidodecadodecahedron	Icosidodecadodecahedron
Rhombicosahedron	Compound of ten triangular prisms	Compound of twenty triangular prisms

v t e Star-polyhedra navigator

Kepler-Poinsot polyhedra (Nonconvex regular polyhedra)	small stellated dodecahedron great dodecahedron great stellated dodecahedron great icosahedron

Uniform truncations of Kepler-Poinsot polyhedra	dodecadodecahedron truncated great dodecahedron rhombidodecadodecahedron Truncated dodecadodecahedron snub dodecadodecahedron great icosidodecahedron truncated great icosahedron nonconvex great rhombicosidodecahedron great truncated icosidodecahedron

Nonconvex uniform Hemipolyhedra	tetrahemihexahedron cubohemioctahedron octahemioctahedron small dodecahemidodecahedron small icosihemidodecahedron great dodecahemidodecahedron great icosihemidodecahedron great dodecahemicosahedron small dodecahemicosahedron

Duals of nonconvex uniform polyhedra	medial rhombic triacontahedron small stellapentakis dodecahedron medial deltoidal hexecontahedron small rhombidodecacron medial pentagonal hexecontahedron medial disdyakis triacontahedron great rhombic triacontahedron great stellapentakis dodecahedron great deltoidal hexecontahedron great disdyakis triacontahedron great pentagonal hexecontahedron

Duals of Nonconvex uniform (Infinite stellations)	tetrahemihexacron hexahemioctacron octahemioctacron small dodecahemidodecacron small icosihemidodecacron great dodecahemidodecacron great icosihemidodecacron great dodecahemicosacron small dodecahemicosacron

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