Tetracontafold octaswirlchoron

The tetracontafold octaswirlchoron is an isogonal polychoron with 480 tetragonal disphenoids, 1920 phyllic disphenoids of two kinds, and 240 vertices. 8 tetragonal and 32 phyllic disphenoids join at each vertex. It is the tenth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{4-\sqrt{5+\sqrt5}}{4-\sqrt{8+2\sqrt{10+2\sqrt5}}}}$$ ≈ 1:5.15761.

Vertex coordinates
Coordinates for the vertices of a tetracontafold 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 19.
 * ±(0, 0, sin(kπ/20), cos(kπ/20)),
 * ±(sin(kπ/20), cos(kπ/20), 0, 0),
 * ±(sin(kπ/20)/$\sqrt{2}$, cos(kπ/20)/$\sqrt{2}$, cos(kπ/20)/$\sqrt{2}$, sin(kπ/20)/$\sqrt{2}$),