Octadecafold tetraswirlchoron

The octadecafold tetraswirlchoron is an isogonal polychoron with 72 triangular gyroprisms, 216 phyllic disphenoids, and 72 vertices. 6 triangular gyroprisms and 12 phyllic disphenoids join at each vetex. It is the ninth in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\csc\frac{\pi}{18}}{2}$$ ≈ 1:2.87939.

Vertex coordinates
Coordinates for the vertices of an octadecafold tetraswirlchoron of circumradius 1, centered at the origin, are given by: along with 120° and 240° rotations in the xy axis of: where k is an integer from 0 to 8.
 * ±(0, 0, sin(kπ/9), cos(kπ/9)),
 * ±($\sqrt{6}$sin(kπ/9)/3, $\sqrt{6}$cos(kπ/9)/3, $\sqrt{3}$cos(kπ/9)/3, $\sqrt{3}$sin(kπ/9)/3),