Medial rhombic triacontahedron
| Medial rhombic triacontahedron | |
|---|---|
 | |
| Type | Star polyhedron |
| Face |  |
| 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.
Stellation
The Medial rhombic triacontahedron is a stellation of the rhombic triacontahedron. The convex hull of the dodecadodecahedron is an icosidodecahedron.
Related hyperbolic tiling
It is topologically equivalent to a quotient space of 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, and a quotient space of the order-4 pentagonal tiling 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, MR 730208
- ↑ The Regular Polyhedra (of index two), David A. Richter