Great octadecafold triantiprismatoswirlchoron

The octadecafold triantiprismatoswirlchoron is an isogonal polychoron with 36 triangular antiprisms, 216 phyllic disphenoids of two kinds, 216 irregular tetrahedra and 108 vertices. It is the third in an infinite family of isogonal triangular antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:2.47578, where a is the second largest positive real root of 37x12-846x10+5520x8-12382x6+11898x4-5001x2+757.

Vertex coordinates
Coordinates for the vertices of a dodecafold triantiprismatoswirlchoron, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of: where a = $\sqrt{3}$/3, b = (3+$\sqrt{13-8cos(2π/9)}$)/(2$\sqrt{3}$cos(π/9)+6sin(π/9)) and k is an integer from 0 to 8.
 * ±(a*sin(kπ/6), a*cos(kπ/6), b*cos(kπ/6), b*sin(kπ/6)),
 * ±(b*sin((k+2)π/6), b*cos((k+2)π/6), a*cos(kπ/6), a*sin(kπ/6)),