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.

Rhombicosahedron
TypeUniform star polyhedron
ElementsF = 50, E = 120
V = 60 (χ = 10)
Faces by sides30{4}+20{6}
Wythoff symbol
Symmetry groupIh, [5,3], *532
Index referencesU56, C72, W96
Dual polyhedronRhombicosacron
Vertex figure
4.6.4/3.6/5
Bowers acronymRi
3D model of a rhombicosahedron

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
TypeStar polyhedron
Face
ElementsF = 60, E = 120
V = 50 (χ = 10)
Symmetry groupIh, [5,3], *532
Index referencesDU56
dual polyhedronRhombicosahedron
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.


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