Triangular-hexagonal tetraswirlprism

The triangular-hexagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 12 hexagonal gyroprisms, 24 triangular gyroprisms, and 216 phyllic disphenoids of three kinds. 2 hexagonal gyroprisms, 2 triangular gyroprisms, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the dodecagonal-icositetragonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{6}{16-3\sqrt2-2\sqrt3-3\sqrt6}}$$ ≈ 1:2.52005.