Hexecontafold icosaswirlchoron

The hexecontafold icosaswirlchoron is an isogonal polychoron with 1200 triangular gyroprisms, 1800 rhombic disphenoids, and 720 vertices. 10 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