Pentagonal duotransitionalterprism

The pentagonal duotransitionalterprism is a convex isogonal polychoron and the third member of the duotransitionalterprism family. It consists of 10 pentagonal trapezorhombihedra, 10 pentagonal prisms, and 25 rectangular trapezoprisms. 2 pentagonal trapezorhombihedra, 1 pentagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal pentagonal-decagonal duoprisms. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{3+sqrt\5}}{2}$$ ≈ 1:2.14412.