Hexagonal-snub cubic duoantiprism

The hexagonal-snub cubic duoantiprism is a convex isogonal polyteron that consists of 12 snub cubic antiprisms, 6 square-hexagonal duoantiprisms, 8 triangular-hexagonal duoantiprisms, 12 digonal-hexagonal duoantiprisms and 288 mirror-symmetric pentachora obtained through the process of alternating the dodecagonal-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:$$\sqrt{\frac{66+26\sqrt3+\sqrt{1922+1104\sqrt3}}{97}}$$ ≈ 1:1.33530.