# 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

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.