Hexagonal ditetragoltriate

The hexagonal ditetragoltriate is a convex isogonal polychoron and the fourth member of the ditetragoltriates that consists of 12 hexagonal prisms and 36 rectangular trapezoprisms. However, it cannot be made uniform. It is the first in an infinite family of isogonal hexagonal prismatic swirlchora.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt2}{2}$$ ≈ 1:1.70711.

Vertex coordinates
The vertices of a hexagonal ditetragoltriate, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by:
 * (0, ±1, 0, ±(2+$\sqrt{2}$)/2),
 * (0, ±1, ±$\sqrt{18+12√2}$/4, ±(2+$\sqrt{2}$)/4),
 * (±$\sqrt{3}$/2, ±1/2, 0, ±(2+$\sqrt{2}$)/2),
 * (±$\sqrt{3}$/2, ±1/2, ±$\sqrt{18+12√2}$/4, ±(2+$\sqrt{2}$)/4),
 * (0, ±(2+$\sqrt{2}$)/2, 0, ±1),
 * (0, ±(2+$\sqrt{2}$)/2, ±$\sqrt{3}$/2, ±1/2),
 * (±$\sqrt{18+12√2}$/4, ±(2+$\sqrt{2}$)/4, 0, ±1),
 * (±$\sqrt{18+12√2}$/4, ±(2+$\sqrt{2}$)/4, ±$\sqrt{3}$/2, ±1/2).