Transitional triangular double tetraswirlprism

The transitional triangular double tetraswirlprism is an isogonal polychoron with 24 triangular gyroprisms, 36 rectangular gyroprisms, and 36 rhombic disphenoids. 2 triangular gyroprisms, 4 rectangular gyroprisms, and 2 rhombic disphenoids 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 great triangular double tetraswirlprism.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{286+156\sqrt3}}{13}$$ ≈ 1:1.81415.

Vertex coordinates
Coordinates for the vertices of a transitional triangular double tetraswirlprism, centered at the origin, are given by, along with their 180° rotations in the xy axis of: where a = $\sqrt{65-26√3}$/13, b = $\sqrt{104+26√3}$/13 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)),