Icosidifold tetraswirlchoron

The icosidifold tetraswirlchoron is an isogonal polychoron with 792 phyllic disphenoids of three kinds and 88 vertices. 36 disphenoids join at each vertex. It is the eleventh in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{3-\sqrt3\cos\frac{5\pi}{22}}}{\sqrt6\sin\frac{\pi}{22}}$$ ≈ 1:3.73032.

Vertex coordinates
Coordinates for the vertices of an icosidifold 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 10.
 * ±(0, 0, sin(kπ/11), cos(kπ/11)),
 * ±($\sqrt{6}$sin(kπ/11)/3, $\sqrt{6}$cos(kπ/11)/3, $\sqrt{3}$cos(kπ/11)/3, $\sqrt{3}$sin(kπ/11)/3),