Pentagonal-snub cubic duoantiprism

The pentagonal-snub cubic duoantiprism, or pesnicdap, is a convex isogonal polyteron that consists of 10 snub cubic antiprisms, 6 square-pentagonal duoantiprisms, 8 triangular-pentagonal duoantiprisms, 12 digonal-pentagonal duoantiprisms, and 240 sphenoidal pyramids. 2 snub cubic antiprisms, 1 square-pentagonal duoantiprism, 1 triangular-pentagonal duoantiprism, 1 digonal-pentagonal duoantiprism, and 5 sphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the decagonal-great rhombicuboctahedral duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{85+30\sqrt2+\sqrt{655+450\sqrt2}}{93}}$$ ≈ 1:1.32536.