Snub square prismantiprismoid

The snub square prismantiprismoid is a convex isogonal polychoron that consists of 32 square antiprisms of two kinds, 32 tetragonal disphenoids, and 128 irregular tetrahedra. 4 triangular gyroprisms, 2 tetragonal disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained from the process of alternating a triangular truncatoprismantiprismoid. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{7+4\sqrt{2}}}{2}$$ ≈ 1:1.77882.