Great octadecafold triantiprismatoswirlchoron

The great octadecafold triantiprismatoswirlchoron is an isogonal polychoron with 36 triangular antiprisms, 216 phyllic disphenoids of two kinds, 432 irregular tetrahedra of two kinds and 108 vertices. It is the third in an infinite family of isogonal triangular antiprismatic swirlchora, the others being the small octadecafold triantiprismatoswirlchoron, small transitional octadecafold triantiprismatoswirlchoron and great transitional octadecafold triantiprismatoswirlchoron.

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 great octadecafold 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/9), a*cos(kπ/9), b*cos(kπ/9), b*sin(kπ/9)),
 * ±(b*sin((k+3)π/9), b*cos((k+3)π/9), a*cos(kπ/9), a*sin(kπ/9)),