Square truncatoprismantiprismoid

The square truncatoprismantiprismoid is a convex isogonal polychoron that consists of 16 ditetragonal prisms, 16 ditetragonal trapezoprisms and 32 rectangular trapezoprisms. However, it cannot be made uniform.

This polychoron can be alternated into a snub square prismantiprismoid, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{4+2\sqrt2}}{2}$$ ≈ 1:2.30656.

Vertex coordinates
The vertices of a square truncatoprismantiprismoid, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by two Cartesian products of two identical ditetragons of length 1 and $$\frac{2+\sqrt{4+2\sqrt2}}{2}$$ where the bases of the second Cartesian product are rotated 45 degrees.