Triangular ditetragoltriate

The triangular ditetragoltriate is a convex isogonal polychoron and the first member of the ditetragoltriates that consists of 6 triangular prisms and 9 rectangular trapezoprisms. However, it cannot be made uniform. It is the first in an infinite family of isogonal triangular prismatic swirlchora.

Within the representation ab3oo ba3oo&#zc, a<b, it happens that c=(b-a) $\sqrt{2/3}$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt6}{2}$$ ≈ 1:2.22474.

Vertex coordinates
The vertices of a triangular ditetragoltriate, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by:
 * (0, $\sqrt{3}$/3, 0, $\sqrt{30+12√6}$/6),
 * (0, $\sqrt{3}$/3, ±(2+$\sqrt{6}$)/4, -$\sqrt{30+12√6}$/12),
 * (0, $\sqrt{30+12√6}$/6, 0, $\sqrt{3}$/3),
 * (0, $\sqrt{30+12√6}$/6, ±1/2, -$\sqrt{3}$/6),
 * (±1/2, -$\sqrt{3}$/6, 0, $\sqrt{30+12√6}$/6),
 * (±1/2, -$\sqrt{3}$/6, ±(2+$\sqrt{6}$)/4, -$\sqrt{30+12√6}$/12),
 * (±(2+$\sqrt{6}$)/4, -$\sqrt{30+12√6}$/12, 0, $\sqrt{3}$/3),
 * (±(2+$\sqrt{6}$)/4, -$\sqrt{30+12√6}$/12, ±1/2, -$\sqrt{3}$/6).