Square duotransitionalterprism

The square duotransitionalterprism is a convex isogonal polychoron and the second member of the duotransitionalterprism family. It consists of 8 square trapezorhombihedra, 8 square prisms, and 16 rectangular trapezoprisms. 2 square trapezorhombihedra, 1 square prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal square-octagonal duoprisms. However, it cannot be made scaliform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:2.

Vertex coordinates
The vertices of a square duotransitionalterprism, assuming that the isosceles trapezoids have three equal edges of length 1, centered at the origin, are given by:
 * $$\left(±1,\,±1,\,±\frac12,\,±\frac32\right),$$
 * $$\left(±1,\,±1,\,±\frac32,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac32,\,±1,\,±1\right),$$
 * $$\left(±\frac32,\,±\frac12,\,±1,\,±1\right).$$