Square-pentagonal tetraswirlprism

The square-pentagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 16 pentagonal gyroprisms, 20 square gyroprisms, and 240 phyllic disphenoids of three kinds. 2 pentagonal gyroprisms, 2 square gyroprisms, and 12 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the hexadecagonal-icosagonal duoprism.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{20}{40+4\sqrt5-10\sqrt{2+\sqrt2}-5\sqrt{10+2\sqrt5}-\sqrt{50+10\sqrt5}}}$$ ≈ 1:2.60863.