Triangular duotruncatoalterprism

The triangular duotruncatoalterprism is a convex isogonal polychoron and the first member of the duotruncatoalterprism family. It consists of 6 triangular prisms, 12 triangular cupolas, 9 rectangular trapezoprisms, and 9 tetragonal disphenoids. 1 triangular prism, 3 triangular cupolas, 2 rectangular trapezoprisms, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal triangular-hexagonal duoprisms. However, it cannot be made scaliform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$$\frac{2+\sqrt2}{2}$$ ≈ 1:1.70711) would yield a triangular duotransitionalterprism instead.