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.

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:

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

External links

• Weisstein, Eric W. "Medial Rhombic Triacontahedron". MathWorld.
• Uniform polyhedra and duals