Hexagonal duotransitionalterprism

The hexagonal duotransitionalterprism is a convex isogonal polychoron and the fifth member of the duotransitionalterprism family. It consists of 12 hexagonal trapezorhombihedra, 12 hexagonal prisms, and 36 rectangular trapezoprisms. 2 hexagonal trapezorhombihedra, 1 hexagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal hexagonal-dihexagonal duoprisms. However, it cannot be made scaliform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt6}{2}$$ ≈ 1:2.22474.