Triangular duotransitionalterprism

The triangular duotransitionalterprism is a convex isogonal polychoron and the first member of the duotransitionalterprism family. It consists of 6 triangular trapezorhombihedra, 6 triangular prisms, and 9 rectangular trapezoprisms. 2 triangular trapezorhombihedra, 1 triangular prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal triangular-hexagonal duoprisms. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt2}{2}$$ ≈ 1:1.70711.