Great triangular double tetraswirlprism

The triangular double tetraswirlprism is an isogonal polychoron with 24 triangular antiprisms, 36 rhombic disphenoids, 144 phyllic disphenoids of two kinds, 144 irregular tetrahedra and 72 vertices. It is the fourth in an infinite family of isogonal triangular prismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is $$1:\tfrac{\sqrt{10+4\sqrt3}}{2} ≈ 1:2.05719$$.

Vertex coordinates
Coordinates for the vertices of a dodecafold triprismatoswirlchoron, centered at the origin, are given by, along with their 180° rotations in the xy axis of: where a = 1/2, b = $\sqrt{3}$/2 and k is an integer from 0 to 5.
 * ±(a*sin(kπ/6), a*cos(kπ/6), b*cos(kπ/6), b*sin(kπ/6)),
 * ±(b*sin(kπ/6), b*cos(kπ/6), a*cos(kπ/6), a*sin(kπ/6)),