Tetrafold tetraswirlchoron

The tetrafold tetraswirlchoron is an isogonal polychoron with 24 tetragonal disphenoids, 48 phyllic disphenoids and 16 vertices. It is the second in an infinite family of isogonal tetrahedral swirlchora.

Vertex coordinates
Coordinates for the vertices of a tetrafold tetraswirlchoron of circumradius 1, centered at the origin, are:
 * (0, 0, 0, ±1),
 * (0, 0, ±1, 0),
 * ±(0, $\sqrt{6}$/3, $\sqrt{3}$/3, 0),
 * ±($\sqrt{6}$/3, 0, 0, $\sqrt{3}$/3),
 * ±($\sqrt{6}$/6, $\sqrt{2}$/2, 0, –$\sqrt{3}$/3),
 * ±($\sqrt{6}$/6, –$\sqrt{2}$/2, 0, –$\sqrt{3}$/3),
 * ±($\sqrt{2}$/2, $\sqrt{6}$/6, –$\sqrt{3}$/3, 0),
 * ±($\sqrt{2}$/2, –$\sqrt{6}$/6, $\sqrt{3}$/3, 0).

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Edge (16): Tetrafold tetraswirlchoron
 * Edge (24): Icositetrachoron
 * Edge (48): Dodecafold tetraswirlchoron