Octafold tetraswirlchoron

The octafold tetraswirlchoron is an isogonal polychoron with 48 rhombic disphenoids, 96 phyllic disphenoids, and 32 vertices. 6 rhombic and 12 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal tetrahedral swirlchora.

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