Triangular-gyroprismatic hexacosichoron

The triangular-antiprismatic hexacosichoron, also known as the ikeswirl 600, is a noble polychoron with 600 triangular antiprisms and 360 vertices. It is the third in an infinite family of isogonal icosahedral swirlchora and also the first in an infinite family of isochoric icosahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{225+75\sqrt5+5\sqrt{1950+870\sqrt5}}}{10}$$ ≈ 1:2.65475.

Vertex coordinates
Coordinates for the vertices of a triangular-antiprismatic hexacosichoron 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 14.
 * ±(0, 0, sin(kπ/15), cos(kπ/15)),
 * ±(cos(kπ/15), sin(kπ/15), 0, 0),
 * ±(2sin(kπ/15)/$\sqrt{10+2√5}$, 2cos(kπ/15)/$\sqrt{10+2√5}$, 2cos(kπ/15)/$\sqrt{10-2√5}$, 2sin(kπ/15)/$\sqrt{10-2√5}$),
 * ±(2sin(kπ/15)/$\sqrt{10-2√5}$, 2cos(kπ/15)/$\sqrt{10-2√5}$, -2cos(kπ/15)/$\sqrt{10+2√5}$, -2sin(kπ/15)/$\sqrt{10+2√5}$),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular antiprism (600): Pentagonal-antiprismatic triacosihexecontachoron
 * Triangle (600): Pentagonal-antiprismatic triacosihexecontachoron
 * Edge (360): Triangular-antiprismatic hexacosichoron