Rhombicosacron

In geometry, the rhombicosacron (or midly dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces.

Proportions
Each face has two angles of $$\arccos(\frac{3}{4})\approx 41.409\,622\,109\,27^{\circ}$$ and two angles of $$\arccos(-\frac{1}{6})\approx 99.594\,068\,226\,86^{\circ}$$. The diagonals of each antiparallelogram intersect at an angle of $$\arccos(\frac{1}{8}+\frac{7\sqrt{5}}{24})\approx 38.996\,309\,663\,87^{\circ}$$. The dihedral angle equals $$\arccos(-\frac{5}{7})\approx 135.584\,691\,402\,81^{\circ}$$. The ratio between the lengths of the long edges and the short ones equals $$\frac{3}{2}+\frac{1}{2}\sqrt{5}$$, which is the square of the golden ratio.