# Rhombicosahedron

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

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.

3D model of a rhombicosahedron

## 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, [5,3], *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.