Pentagonal-hexagonal duoantiprismatic antiprism

The pentagonal-hexagonal duoantiprismatic antiprism, or phiddapap, is a convex isogonal polyteron that consists of 2 pentagonal-hexagonal duoantiprisms, 10 digonal-hexagonal duoantiprisms, 12 digonal-pentagonal duoantiprisms, and 120 digonal disphenoidal pyramids. 1 pentagonal-hexagonal duoantiprisms, 2 digonal-hexagonal duoantiprisms, 2 digonal-pentagonal duoantiprisms, and 5 digonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the decagonal-dodecagonal duoprismatic prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{400+165\sqrt3+\sqrt{19955+11500\sqrt3}}{482}}$$ ≈ 1:1.35539.