Icosafold icosaswirlchoron

The icosafold icosaswirlchoron is an isogonal polychoron with 600 tetragonal disphenoids, 1200 phyllic disphenoids, and 240 vertices. 10 tetragonal and 20 phyllic disphenoids join at each vertex.

It is the second in an infinite family of isogonal icosahedral swirlchora and one of several polychora formed as the hull of various combinations of 2 hexacosichora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt{10+2\sqrt5}}}{2}$$ ≈ 1:1.97538.

Vertex coordinates
Coordinates for the vertices of an icosafold 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 9.
 * ±(0, 0, sin(kπ/10), cos(kπ/10)),
 * ±(cos(kπ/10), sin(kπ/10), 0, 0),
 * ±(2sin(kπ/10)/$\sqrt{10+2√5}$, 2cos(kπ/10)/$\sqrt{10+2√5}$, 2cos(kπ/10)/$\sqrt{10-2√5}$, 2sin(kπ/10)/$\sqrt{10-2√5}$),
 * ±(2sin(kπ/10)/$\sqrt{10-2√5}$, 2cos(kπ/10)/$\sqrt{10-2√5}$, -2cos(kπ/10)/$\sqrt{10+2√5}$, -2sin(kπ/10)/$\sqrt{10+2√5}$),