Looking into the Tetartoid, which is a version of the Dodecahedron where all pentagons are not regular, described in the answer by Aretino here is a way to construct it from a Tetrahedron.
Similarly, the asymmetric version of a Trigonal Trapezohedron is a relaxation of the conditions of a cube where the faces don't have to be regular (only two adjacent ones need to be). I feel there must be a way to similarly construct it from a platonic solid as well.
Also, Aretino links to this page where the construction of the Tetartoid is described. And in the section "4t", there does appear to be a solid that "looks like" the Trigonal Trapezahedron. But I can't be sure if it's even convex.
So my question is, does a corresponding construction exist for the asymmetric version of the Trigonal Trapezahedron from a Platonic solid?
