Snub digonal-square prismantiprismoid

The snub digonal-square prismantiprismoid is a convex isogonal polychoron that consists of 4 square antiprisms, 4 square gyroprisms, 8 tetragonal disphenoids, 8 rhombic disphenoids, 16 phyllic disphenoids, and 64 irregular tetrahedra of two kinds. 1 square antiprism, 1 square gyroprism, 1 tetragonal disphenoid, 1 rhobic disphenoid, 2 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained from the process of alternating a digonal-square truncatoprismantiprismoid. However, it cannot be made uniform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$$\sqrt{1+\sqrt2}$$ ≈ 1:1.55377) would yield a square-square duoantiprism instead.