Great rhombic triacontahedron

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

If its dual, the great icosidodecahedron, has an edge length of 1, then the edges of the rhombi will measure $$\frac{\sqrt{10\left(5-\sqrt5\right)}}{8} ≈ 0.65716$$. ​The rhombus faces will have length $$\frac{\sqrt5}{2} ≈ 1.11803$$, and width $$\frac{5-\sqrt5}{4} ≈ 0.69098$$. The rhombi have two interior angles of $$\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$$, and one of $$\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$$.

Vertex coordinates
A great rhombic triacontahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{5-\sqrt5}{8},\,±\frac{3\sqrt5-5}{8},\,0\right),$$
 * $$\left(±\frac{3\sqrt5-5}{8},\,±\frac{\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac{5-\sqrt5}{8},\,±\frac{5-\sqrt5}{8},\,±\frac{5-\sqrt5}{8}\right).$$