Triangular-gyroprismatic enneacontahexachoron

The triangular-antiprismatic enneacontahexachoron, also known as the octswirl 96, is a noble polychoron with 96 triangular antiprisms and 72 vertices. It is the first in an infinite family of isochoric cubic swirlchora and also the third in an infinite family of isogonal octahedral swirlchora.

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

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular antiprism (96): Square-antiprismatic heptacontadichoron
 * Triangle (96): Square-antiprismatic heptacontadichoron
 * Edge (72): Triangular-antiprismatic enneacontahexachoron