Icosioctafold octaswirlchoron

The icosioctafold octaswirlchoron is an isogonal polychoron with 1344 phyllic disphenoids of two kinds and 168 vertices. 32 disphenoids join at each vertex. It is the seventh 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 an icosioctafold 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 13.
 * ±(0, 0, sin(kπ/14), cos(kπ/14)),
 * ±(sin(kπ/14), cos(kπ/14), 0, 0),
 * ±(sin((k+1/2)π/14)/$\sqrt{2}$, cos((k+1/2)π/14)/$\sqrt{2}$, cos((k+1/2)π/14)/$\sqrt{2}$, sin((k+1/2)π/14)/$\sqrt{2}$),