It is topologically equivalent to a quotient space of the hyperbolic order-4 pentagonal tiling, by distorting the pentagrams back into regular pentagons. As such, it is topologically a regular polyhedron of index two:  The colours in the above image correspond to the red pentagrams and yellow pentagons of the dodecadodecahedron at the top of this article. 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. The "medial rhombic triacontahedron" is a stellation of the rhombic triacontahedron, which is the dual of the icosidodecahedron, the convex hull of the dodecadodecahedron (dual to the original medial rhombic triacontahedron). 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.