Square-hexagonal tetraswirlprism

The square-hexagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 16 hexagonal gyroprisms, 24 square gyroprisms, and 288 phyllic disphenoids of three kinds. 2 hexagonal gyroprisms, 2 square gyroprisms, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the hexadecagonal-icositetragonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2}{6-\sqrt2-\sqrt6-\sqrt{2+\sqrt2}}}$$ ≈ 1:2.63278.