Medial 15-4 double step prism

The medial 15-4 double step prism is a convex isogonal polychoron that consists of 15 rhombic disphenoids, 120 phyllic disphenoids of four kinds, and 60 irregular tetrahedra. 2 rhombic disphenoids, 16 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal 15-4 step prisms.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{979-33\sqrt5+22\sqrt{1590-18\sqrt5}}}{22}$$ ≈ 1:1.91303.