Medial rhombic triacontahedron: Difference between revisions
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It is topologically equivalent to the [[hyperbolic geometry|hyperbolic]] [[order-5 square tiling]], by distorting the rhombi into [[square (geometry)|squares]]. As such, it is topologically a [[regular polyhedron]] of index two:<ref>[http://homepages.wmich.edu/~drichter/regularpolyhedra.htm The Regular Polyhedra (of index two)], David A. Richter</ref> |
It is topologically equivalent to the [[hyperbolic geometry|hyperbolic]] [[order-5 square tiling]], by distorting the rhombi into [[square (geometry)|squares]]. As such, it is topologically a [[regular polyhedron]] of index two:<ref>[http://homepages.wmich.edu/~drichter/regularpolyhedra.htm The Regular Polyhedra (of index two)], David A. Richter</ref> |
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[[File:Uniform tiling |
[[File:Uniform tiling 45-t0.png|250px]] |
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Note that the order-5 square tiling is dual to the [[order-4 pentagonal tiling]], which is topologically equivalent to the dual of the medial rhombic triacontahedron, the [[dodecadodecahedron]]. |
Note that the order-5 square tiling is dual to the [[order-4 pentagonal tiling]], which is topologically equivalent to the dual of the medial rhombic triacontahedron, the [[dodecadodecahedron]]. |
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Revision as of 09:20, 30 August 2011
| Medial rhombic triacontahedron | |
|---|---|
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| Type | Star polyhedron |
| Face | 
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| Elements | F = 30, E = 60 V = 24 (χ = −6) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | DU36 |
| dual polyhedron | Dodecadodecahedron |
In geometry, the medial rhombic triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the dodecadodecahedron. It has 30 intersecting rhombic faces.
It can also be called the small stellated triacontahedron.
It is topologically equivalent to the hyperbolic order-5 square tiling, by distorting the rhombi into squares. As such, it is topologically a regular polyhedron of index two:[1]
Note that the order-5 square tiling is dual to the order-4 pentagonal tiling, which is topologically equivalent to the dual of the medial rhombic triacontahedron, the dodecadodecahedron.
References
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR730208
- ^ The Regular Polyhedra (of index two), David A. Richter
External links
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