Square duotruncatoalterprism

The square duotruncatoalterprism is a convex isogonal polychoron and the third member of the duotruncatoalterprism family. It consists of 8 square prisms, 16 square cupolas, 16 rectangular trapezoprisms, and 16 tetragonal disphenoids. 1 square prism, 3 square cpuolas, 2 rectangular trapezoprisms, and 1 tetragonal disphenoid join at each vertex. It can be obtained as the convex hull of two orthogonal square-ditetragonal duoprisms. However, it cannot be made scaliform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:2) would yield a square duotransitionalterprism instead.