Triangular-square truncatoprismantiprismoid

The triangular-square truncatoprismantiprismoid is a convex isogonal polychoron that consists of 6 ditetragonal prisms, 6 ditetragonal trapezoprisms, 8 ditrigonal prisms, 8 ditrigonal trapezoprisms, and 24 rectangular frustums. 2 rectangular frustums and one of each of the other cell types join at each vertex. It can be obtained as the convex hull of two opposite ditrigonal-ditetragonal duoprisms. However, it cannot be made uniform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately $$2.2636717044314857663608645$$.

Vertex coordinates
The vertices of a triangular-square truncatoprismantiprismoid, assuming that the edge length differences are minimized, centered at the origin, are given as Cartesian products of the vertices of ditetragon DTE1 and ditrigon DTR1, both of lengths 1 and approximately $$2.2636717044314857663608645$$:
 * DTE1 × DTR1,
 * DTE2 × DTR2 (DTE1 rotated 45 degrees and DTR1 rotated 60 degrees).