Square-gyroprismatic heptacontadichoron

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

Vertex coordinates
Coordinates for the vertices of a square-antiprismatic enneacontahexachoron of circumradius $\sqrt{3+√3}$, centered at the origin, are given by reflections through the x=y and z=w hyperplanes and 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, 1, (1+$\sqrt{3}$)/2, (1+$\sqrt{3}$)/2),
 * ((1+$\sqrt{3}$)/2, (1+$\sqrt{3}$)/2, 0, 1),
 * (1/2, $\sqrt{3}$/2, (2+$\sqrt{3}$)/2, 1/2),
 * (1/2, $\sqrt{3}$/2, 1/2, (2+$\sqrt{3}$)/2).

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