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Rhombicosahedron

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Not to be confused with Rhombic icosahedron.
Rhombicosahedron
Type Uniform star polyhedron
Elements F = 50, E = 120
V = 60 (χ = −10)
Faces by sides 30{4}+20{6}
Coxeter diagram (with extra double-covered pentagrams)
(with extra double-covered pentagons)
Wythoff symbol 2 3 (5/4 5/2) |
Symmetry group Ih, , *532
Index references U56, C72, W96
Dual polyhedron Rhombicosacron
Vertex figure
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. 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


Rhombicosacron

Rhombicosacron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 50 (χ = −10)
Symmetry group Ih, , *532
Index references DU56
dual polyhedron Rhombicosahedron
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.

References

  1. Maeder, Roman. "56: rhombicosahedron". MathConsult.

External links

Star-polyhedra navigator
Kepler-Poinsot
polyhedra
(nonconvex
regular polyhedra)
Uniform truncations
of Kepler-Poinsot
polyhedra
Nonconvex uniform
hemipolyhedra
Duals of nonconvex
uniform polyhedra
Duals of nonconvex
uniform polyhedra with
infinite stellations


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