Rhombicosahedron

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Rhombicosahedron
Rhombicosahedron.png
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 Rhombicosahedron vertfig.png
4.6.4/3.6/5
Bowers acronym Ri

In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. Its vertex figure is an antiparallelogram.

Related polyhedra[edit]

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).

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

Rhombicosacron[edit]

Rhombicosacron
DU56 rhombicosacron.png
Type Star polyhedron
Face DU56 facets.png
Elements F = 60, E = 120
V = 50 (χ = −10)
Symmetry group Ih, [5,3], *532
Index references DU56
dual polyhedron Rhombicosahedron

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[edit]

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links[edit]