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In geometry, the medial rhombic triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the dodecadodecahedron. It has 30 intersecting rhombic faces.
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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:
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.