Triangular-gyroprismatic enneacontahexachoron

The triangular-antiprismatic enneacontahexachoron, also known as the octswirl 96, is a noble polychoron with 96 triangular antiprisms and 72 vertices. Together with its dual, it is the third in an infinite family of cubic swirlchora and also the second in an infinite family of octahedral swirlchora.

Vertex coordinates
Coordinates for the vertices of a triangular-antiprismatic enneacontahexachoron of circumradius 1, centered at the origin, are given by: together with reflections through the x=y and z=w hyperplanes, and with all changes of sign, as well as together with reflections through the x=y and z=w hyperplanes, and with all even changes of sign.
 * (1, 0, 0, 0),
 * (0, 0, 1, 0),
 * (1/2, 1/2, 1/2, 1/2),
 * (1/2, $\sqrt{3}$/2, 0, 0),
 * (0, 0, 1/2, $\sqrt{3}$/2),
 * (($\sqrt{3}$–1)/4, ($\sqrt{3}$+1)/4, ($\sqrt{3}$–1)/4, ($\sqrt{3}$+1)/4),