Pentagonal tetraswirlprism

The pentagonal tetraswirlprism is a convex isogonal polychoron and member of the duoprismatic swirlprism family that consists of 40 pentagonal gyroprisms, 100 rhombic disphenoids, and 200 phyllic disphenoids. 4 pentagonal gyroprisms, 4 rhombic disphenoids, and 8 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the icosagonal duoprism. It is the fourth in an infinite family of isogonal pentagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt5+\sqrt{5+2\sqrt5}}{2}$$ ≈ 1:2.65688.