Rhombicosacron

The rhombicosacron is a uniform dual polyhedron. It consists of 60 butterflies.

If its dual, the rhombicosahedron, has an edge length of 1, then the short edges of the butterflies will measure $$\frac{5\sqrt6-\sqrt{30}}{10} ≈ 0.67702$$, and the long edges will be $$\frac{5\sqrt6+\sqrt{30}}{10} ≈ 1.77247$$. The butterflies have two interior angles of $$\arccos\left(\frac34\right) ≈ 41.40962°$$, and one of $$\arccos\left(-\frac16\right) ≈ 99.59407°$$. The intersection has an angle of $$\arccos\left(\frac18+\frac{7\sqrt5}{24}\right) ≈ 38.99631°$$.

Vertex coordinates
A rhombicosacron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac{3\sqrt5}{5},\,0,\,0\right),$$
 * $$\left(±3\frac{5-\sqrt5}{20},\,±\frac{3\sqrt5}{10},\,±3\frac{5+\sqrt5}{20}\right),$$
 * $$\left(±1,\,±1,\,±1\right).$$