Tetracontatetrafold octaswirlchoron

The tetracontatetrafold octaswirlchoron is an isogonal polychoron with 3168 phyllic disphenoids of three kinds, and 264 vertices. 48 disphenoids join at each vertex. It is the eleventh in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{2-\sqrt2\cos\frac{3\pi}{28}}}{2\sin\frac{\pi}{28}}$$ ≈ 1:3.64207.

Vertex coordinates
Coordinates for the vertices of a tetracontatetrafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations and sign changes of: along with 90°, 180° and 270° rotations in the xy axis of: where k is an integer from 0 to 21.
 * ±(0, 0, sin(kπ/22), cos(kπ/22)),
 * ±(sin(kπ/22), cos(kπ/22), 0, 0),
 * ±(sin((k+1/2)π/22)/$\sqrt{2}$, cos((k+1/2)π/22)/$\sqrt{2}$, cos((k+1/2)π/22)/$\sqrt{2}$, sin((k+1/2)π/22)/$\sqrt{2}$),