Triangular-gyroprismatic enneacontahexachoron

The triangular-antiprismatic enneacontoctachoron, also known as the octswirl 96 is an isogonal polychoron with 72 tetrahedra of four types and 16 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
The vertices of a triangular-antiprismatic enneacontoctachoron of circumradius 1, centered at the origin, are:
 * (0, 0, 0, ±1)
 * (0, 0, ±1, 0)
 * (0, ±1, 0, 0)
 * (±1, 0, 0, 0)
 * (±1/2, ±1/2, ±1/2, ±1/2)
 * (0, 0, ±1/2, ±$\sqrt{3}$/2)
 * (0, 0, ±$\sqrt{3}$/2, ±1/2)
 * (±1/2, ±$\sqrt{3}$/2, 0, 0)
 * (±$\sqrt{3}$/2, ±1/2, 0, 0)
 * (($\sqrt{3}$-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)
 * (-($\sqrt{3}$-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)
 * (-($\sqrt{3}$-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)
 * (-($\sqrt{3}$-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)
 * (($\sqrt{3}$-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)
 * (($\sqrt{3}$-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)
 * (($\sqrt{3}$-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)
 * (-($\sqrt{3}$-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)
 * (($\sqrt{3}$+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)
 * (($\sqrt{3}$+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)
 * (($\sqrt{3}$+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)
 * (-($\sqrt{3}$+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)
 * (($\sqrt{3}$+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)
 * (-($\sqrt{3}$+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)
 * (-($\sqrt{3}$+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)
 * (-($\sqrt{3}$+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)