Icosafold tetraswirlchoron

The icosafold tetraswirlchoron is an isogonal polychoron with 120 tetragonal disphenoids, 480 phyllic disphenoids of two kinds, and 80 vertices. 6 tetragonal and 24 phyllic disphenoids join at each vertex. It is the tenth in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{12-\sqrt3-\sqrt{15}}{12-3\sqrt{10+2\sqrt5}}}$$ ≈ 1:3.29975.

Vertex coordinates
Coordinates for the vertices of an icosafold 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 9.
 * ±(0, 0, sin(kπ/10), cos(kπ/10)),
 * ±($\sqrt{6}$sin(kπ/10)/3, $\sqrt{6}$cos(kπ/10)/3, $\sqrt{3}$cos(kπ/10)/3, $\sqrt{3}$sin(kπ/10)/3),