Pentagonal-hexagonal tetraswirlprism

The pentagonal-hexagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic tetraswirlprism family that consists of 20 hexagonal gyroprisms, 24 pentagonal gyroprisms, and 360 phyllic disphenoids of three kinds. 2 hexagonal gyroprisms, 2 pentagonal gyroprisms, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the icosagonal-icositetragonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{20}{60-10\sqrt2+4\sqrt5-10\sqrt6-5\sqrt{10+2\sqrt5}-\sqrt{50+10\sqrt5}}}$$ ≈ 1:2.68240.