Dodecafold tetraswirlchoron

The dodecafold tetraswirlchoron is an isogonal polychoron with 48 triangular antiprisms, 72 rhombic disphenoids and 48 vertices. It is the sixth in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{2+\sqrt3}$$ ≈ 1:1.93185.

Vertex coordinates
Coordinates for the vertices of a dodecafold 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 5.
 * ±(0, 0, sin(kπ/6), cos(kπ/6)),
 * ±($\sqrt{6}$sin(kπ/6)/3, $\sqrt{6}$cos(kπ/6)/3, $\sqrt{3}$cos(kπ/6)/3, $\sqrt{3}$sin(kπ/6)/3),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular antiprism (48): Dodecafold tetraswirlchoron
 * Triangle (48): Dodecafold tetraswirlchoron
 * Edge (48): Dodecafold tetraswirlchoron
 * Edge (72): Triangular-antiprismatic enneacontahexachoron
 * Edge (144): Dodecafold truncatotetraswirlchoron