Octadecafold pyritocubiswirlchoron

The octadecafold pyritocubiswirlchoron is an isogonal polychoron with 216 rhombic disphenoids, 864 phyllic disphenoids of two kinds and 144 vertices. It is the third in an infinite family of isogonal pyritohedral cubic swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{4+6\cos\frac{\pi}{9}}{1+2\sin\frac{\pi}{18}}}$$ ≈ 1:2.67464.

Vertex coordinates
Coordinates for the vertices of an octadecafold pyritocubiswirlchoron of circumradius 1, centered at the origin, are: 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)),
 * ±(sin(kπ/9), cos(kπ/9), 0, 0),
 * ±($\sqrt{6}$sin(kπ/9)/3, $\sqrt{6}$cos(kπ/9)/3, $\sqrt{3}$cos(kπ/9)/3, $\sqrt{3}$sin(kπ/9)/3),
 * ±($\sqrt{3}$cos(kπ/9)/3, $\sqrt{3}$sin(kπ/9)/3, -$\sqrt{6}$sin(kπ/9)/3, -$\sqrt{6}$cos(kπ/9)/3),