Square-hexagonal duoantiprismatic antiprism

The square-hexagonal duoantiprismatic antiprism, or shiddapap, is a convex isogonal polyteron that consists of 2 square-hexagonal duoantiprisms, 8 digonal-hexagonal duoantiprisms, 12 digonal-square duoantiprisms, and 96 digonal disphenoidal pyramids. 1 square-hexagonal duoantiprism, 2 digonal-hexagonal duoantiprisms, 2 digonal-square duoantiprisms, and 5 digonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the octagonal-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:$$\sqrt{\frac{66+26\sqrt3+\sqrt{1922+1104\sqrt3}}{97}}$$ ≈ 1:1.33530.