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.

Vertex coordinates
Coordinates for the vertices of a dodecafold tetraswirlchoron of circumradius 1 (and thus edge lengths $$\sqrt{\frac{3-\sqrt3}{2}}$$ and $$\sqrt{2-\sqrt3}$$), centered at the origin, are given by:
 * (0, ±1, 0, 0),
 * (±1, 0, 0, 0),
 * (±1/2, ±$\sqrt{3}$/2, 0, 0),
 * (±$\sqrt{3}$/2, ±1/2, 0, 0)
 * ±(0, $\sqrt{3}$/3, 0, $\sqrt{6}$/3),
 * ±(0, $\sqrt{3}$/3, ±$\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±(±1/2, -$\sqrt{3}$/6, 0, $\sqrt{6}$/3),
 * ±(±1/2, -$\sqrt{3}$/6, ±$\sqrt{2}$/2, -$\sqrt{6}$/6),
 * ±($\sqrt{3}$/3, 0, $\sqrt{6}$/3, 0),
 * ±($\sqrt{3}$/3, 0, -$\sqrt{6}$/6, ±$\sqrt{2}$/2),
 * ±(-$\sqrt{3}$/6, ±1/2, $\sqrt{6}$/3, 0),
 * ±(-$\sqrt{3}$/6, ±1/2, -$\sqrt{6}$/6, ±$\sqrt{2}$/2).

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