Octafold tetraswirlchoron

The octafold tetraswirlchoron is an isogonal polychoron with 48 tetragonal disphenoids, 96 phyllic disphenoids and 32 vertices. It is the fourth in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{18+9\sqrt2-6\sqrt{9+6\sqrt2}}}{3}$$ ≈ 1:1.42140.

Vertex coordinates
Coordinates for the vertices of an octafold tetraswirlchoron of circumradius 1, centered at the origin, are given by: along with 120° and 240° rotations in the xy axis of: where k is an integer from 0 to 3.
 * ±(0, 0, sin(kπ/4), cos(kπ/4)),
 * ±($\sqrt{6}$sin(kπ/4)/3, $\sqrt{6}$cos(kπ/4)/3, $\sqrt{3}$cos(kπ/4)/3, $\sqrt{3}$sin(kπ/4)/3),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Edge (32): Octafold tetraswirlchoron
 * Edge (48): Octafold ambotetraswirlchoron
 * Edge (96): Octafold truncatotetraswirlchoron