Pentagonal double gyroantiprismoid

The pentagonal double gyroantiprismoid is a convex isogonal polychoron and the fourth member of the double gyroantiprismoid family. It consists of 20 pentagonal antiprisms, 50 tetragonal disphenoids, 100 rhombic disphenoids, and 200 sphenoids. 2 pentagonal antiprisms, 2 tetragonal disphenoids, 4 rhombic disphenoids, and 8 sphenoids join at each vertex. However, it cannot be made uniform. It is the second in an infinite family of isogonal pentagonal prismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{50-5\sqrt5+5\sqrt{50-20\sqrt5}}}{5}$$ ≈ 1:1.41855.