Rhombicosahedron
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, [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.
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
- ^ Maeder, Roman. "56: rhombicosahedron". MathConsult.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
External links
- Weisstein, Eric W. "Rhombicosacron". MathWorld.
- Weisstein, Eric W. "Rhombicosahedron". MathWorld.
- Uniform polyhedra and duals
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polyhedra (nonconvex
regular polyhedra)
of Kepler-Poinsot
polyhedra
hemipolyhedra
uniform polyhedra
- medial rhombic triacontahedron
- small stellapentakis dodecahedron
- medial deltoidal hexecontahedron
- small rhombidodecacron
- medial pentagonal hexecontahedron
- medial disdyakis triacontahedron
- great rhombic triacontahedron
- great stellapentakis dodecahedron
- great deltoidal hexecontahedron
- great disdyakis triacontahedron
- great pentagonal hexecontahedron
uniform polyhedra with
infinite stellations
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