Triacontahexafold cubiswirlchoron

The triacontahexafold cubiswirlchoron is an isogonal polychoron with 216 square gyroprisms, 864 phyllic disphenoids, and 288 vertices. 6 square gyroprisms and 12 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal cubic swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{3-sqrt\3}}{2\sqrt3\sin\frac{\pi}{36}}$$ ≈ 1:3.72962.

Vertex coordinates
Coordinates for the vertices of a triacontahexafold cubiswirlchoron of circumradius 1, centered at the origin, are given by (along with their 90°, 180° and 270° rotations in the xy axis): where k is an integer from 0 to 17.
 * $$\left(\frac{\sin\left((k+1)\pi/18\right)}{\sqrt{3+\sqrt3}},\,\frac{\cos\left((k+1)\pi/18\right)}{\sqrt{3+\sqrt3}},\,\frac{\cos\left((k+1)\pi/18\right)}{\sqrt{3-\sqrt3}},\,\frac{\sin\left((k+1)\pi/18\right)}{\sqrt{3-\sqrt3}}\right),$$
 * $$\left(\frac{\sin\left((k+1)\pi/18\right)}{\sqrt{3-\sqrt3}},\,\frac{\cos\left((k+1)\pi/18\right)}{\sqrt{3-\sqrt3}},\,\frac{\cos\left((k+1)\pi/18\right)}{\sqrt{3+\sqrt3}},\,\frac{\sin\left((k+1)\pi/18\right)}{\sqrt{3+\sqrt3}}\right),$$