Dodecafold tetraswirlchoron

The dodecafold tetraswirlchoron is an isogonal polychoron with 48 triangular gyroprisms, 72 rhombic disphenoids, and 48 vertices. 6 triangular gyroprisms and 6 rhombic disphenoids join at each vertex. 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 gyroprism (48): Dodecafold tetraswirlchoron
 * Triangle (48): Dodecafold tetraswirlchoron
 * Edge (48): Dodecafold tetraswirlchoron
 * Edge (72): Triangular-antiprismatic enneacontahexachoron
 * Edge (144): Dodecafold truncatotetraswirlchoron