Dodecagonal ditetragoltriate

The dodecagonal ditetragoltriate is a convex isogonal polychoron and the tenth member of the ditetragoltriates that consists of 24 dodecagonal prisms and 144 rectangular trapezoprisms. However, it cannot be made uniform. It is the first in an infinite family of isogonal dodecagonal prismatic swirlchora.

This polychoron can be alternated into a hexagonal double antiprismoid, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt3}{2}$$ ≈ 1:1.36603.

Vertex coordinates
The vertices of a dodecagonal ditetragoltriate, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by all permutations of the first and second, as well as the third and fourth coordinates of:
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/4, ±(5+3$\sqrt{3}$)/4),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/4, ±(5+3$\sqrt{3}$)/4),
 * (±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/4, ±(5+3$\sqrt{3}$)/4, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/4, ±(5+3$\sqrt{3}$)/4, ±1/2, ±(2+$\sqrt{3}$)/2).