Decagonal duotransitionalterprism

The decagonal duotransitionalterprism is a convex isogonal polychoron and the ninth member of the duotransitionalterprism family. It consists of 20 decagonal trapezorhombihedra, 20 decagonal prisms, and 100 rectangular trapezoprisms. 2 decagonal trapezorhombihedra, 1 decagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal decagonal-didecagonal duoprisms. However, it cannot be made scaliform.

This polychoron can be alternated into a pentagonal duotransitionalterantiprism, which is also not scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{5+\sqrt5}}{2}$$ ≈ 1:2.34500.