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. 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, [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
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 730208
External links
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