Triangular-square tetraswirlprism

The triangular-square tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 12 square gyroprisms, 16 triangular gyroprisms, and 144 phyllic disphenoids of three kinds. 2 square gyroprisms, 2 triangular gyroprisms, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal-hexadecagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{6}{10-2\sqrt3-3\sqrt{2+\sqrt2}}}$$ ≈ 1:2.45858.