Great triangular double tetraswirlprism

The great triangular double tetraswirlprism is an isogonal polychoron with 24 triangular gyroprisms, 36 rhombic disphenoids, 144 phyllic disphenoids of two kinds, 144 irregular tetrahedra, and 72 vertices. 2 triangular gyroprisms, 6 rhombic disphenoids, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It is the fourth in an infinite family of isogonal triangular prismatic swirlchora, the others being the small triangular double tetraswirlprism and transitional triangular double tetraswirlprism.

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

Vertex coordinates
Coordinates for the vertices of a great triangular double tetraswirlprism optimized via the ratio method, 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)),