Medial rhombic triacontahedron

The medial rhombic triacontahedron is a uniform dual polyhedron. It consists of 30 rhombi.

If its dual, the dodecadodecahedron, has an edge length of 1, then the edges of the rhombi will measure $$\frac{3\sqrt3}{4} ≈ 1.29904$$. ​The rhombus faces will have length $$3\frac{1+\sqrt5}{4} ≈ 2.42705$$, and width $$3\frac{\sqrt5-1}{4} ≈ 0.92705$$. The rhombi have two interior angles of $$\arccos\left(\frac{\sqrt5}{3}\right) ≈ 41.81031°$$, and two of $$\arccos\left(-\frac{\sqrt5}{3}\right) ≈ 138.18969°$$.

Vertex coordinates
A medial rhombic triacontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±3\frac{1+\sqrt5}{8},\,±\frac34,\,0\right),$$
 * $$\left(±\frac34,\,±3\frac{\sqrt5-1}{8},\,0\right).$$

Related polytopes
The medial rhombic triacontahedron is topologically equivalent to a quotient space of the hyperbolic order-5 square tiling, making it abstractly a regular polyhedron.