Heptagonal duotransitionalterprism

The heptagonal duotransitionalterprism is a convex isogonal polychoron and the sixth member of the duotransitionalterprism family. It consists of 14 heptagonal trapezorhombihedra, 14 heptagonal prisms, and 49 rectangular trapezoprisms. 2 heptagonal trapezorhombihedra, 1 heptagoal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal heptagonal-diheptagonal duoprisms. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$1+\sqrt2\cos\frac{\pi}{7}$$ ≈ 1:2.27416.