Tetracontafold icosaswirlchoron

The tetracontafold icosaswirlchoron is an isogonal polychoron with 1200 tetragonal disphenoids, 2400 phyllic disphenoids and 480 vertices. It is the fourth in an infinite family of isogonal icosahedral swirlchora.

Vertex coordinates
Coordinates for the vertices of a tetracontafold icosaswirlchoron of circumradius 1, centered at the origin, are given by: along with 72°, 144°, 216° and 288° rotations in the xy axis of: where k is an integer from 0 to 19.
 * ±(0, 0, sin(kπ/20), cos(kπ/20)),
 * ±(cos(kπ/20), sin(kπ/20), 0, 0),
 * ±(2sin(kπ/20)/$\sqrt{10+2√5}$, 2cos(kπ/20)/$\sqrt{10+2√5}$, 2cos(kπ/20)/$\sqrt{10-2√5}$, 2sin(kπ/20)/$\sqrt{10-2√5}$),
 * ±(2sin(kπ/20)/$\sqrt{10-2√5}$, 2cos(kπ/20)/$\sqrt{10-2√5}$, -2cos(kπ/20)/$\sqrt{10+2√5}$, -2sin(kπ/20)/$\sqrt{10+2√5}$),