Hexecontafold icosaswirlchoron

The hexecontafold icosaswirlchoron is an isogonal polychoron with 1200 triangular gyroprisms, 1800 rhombic disphenoids, and 720 vertices. 1 triangular gyroprisms and 10 rhombic disphenoids join at each vertex. It is the sixth in an infinite family of isogonal icosahedral swirlchora.

Vertex coordinates
Coordinates for the vertices of a hexecontafold 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 29.
 * ±(0, 0, sin(kπ/30), cos(kπ/30)),
 * ±(cos(kπ/30), sin(kπ/30), 0, 0),
 * ±(2sin(kπ/30)/$\sqrt{10+2√5}$, 2cos(kπ/30)/$\sqrt{10+2√5}$, 2cos(kπ/30)/$\sqrt{10-2√5}$, 2sin(kπ/30)/$\sqrt{10-2√5}$),
 * ±(2sin(kπ/30)/$\sqrt{10-2√5}$, 2cos(kπ/30)/$\sqrt{10-2√5}$, -2cos(kπ/30)/$\sqrt{10+2√5}$, -2sin(kπ/30)/$\sqrt{10+2√5}$),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular gyroprism (1200): Hexecontafold dodecaswirlchoron
 * Triangle (1200): Hexecontafold dodecaswirlchoron
 * Edge (720): Hexecontafold icosaswirlchoron