Heptacontafold icosaswirlchoron

The heptacontafold icosaswirlchoron is an isogonal polychoron with 8400 phyllic disphenoids of two kinds and 840 vertices. 40 disphenoids join at each vertex. It is the seventh in an infinite family of isogonal icosahedral swirlchora.

Vertex coordinates
Vertex coordinates for the vertices of a heptacontafold 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 34.
 * $$\pm(0,\,0,\,\sin(k\pi/35),\,\cos(k\pi/35))$$,
 * $$\pm(\cos(k\pi/35),\,\sin(k\pi/35),\,0,\,0)$$,
 * $$\pm\left(\frac{2\sin(k\pi/35)}{\sqrt{10+2\sqrt{5}}},\,\frac{2\cos(k\pi/35)}{\sqrt{10+2\sqrt{5}}},\,\frac{2\sin(k\pi/35)}{\sqrt{10-2\sqrt{5}}},\,\frac{2\cos(k\pi/35)}{\sqrt{10-2\sqrt{5}}}\right)$$
 * $$\pm\left(\frac{2\sin(k\pi/35)}{\sqrt{10-2\sqrt{5}}},\,\frac{2\cos(k\pi/35)}{\sqrt{10-2\sqrt{5}}},\,\frac{2\sin(k\pi/35)}{\sqrt{10+2\sqrt{5}}},\,\frac{2\cos(k\pi/35)}{\sqrt{10+2\sqrt{5}}}\right)$$