Square duotransitionalterprism

The square duotransitionalterprism is a convex isogonal polychoron and the second member of the duotransitionalterprisms that consists of 8 square trapezorhombihedra, 8 square prisms and 16 rectangular trapezoprisms 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:
 * (±1, ±1, ±1/2, ±3/2),
 * (±1, ±1, ±3/2, ±1/2),
 * (±1/2, ±3/2, ±1, ±1),
 * (±3/2, ±1/2, ±1, ±1).