Tetrafold tetraswirlchoron

The tetrafold tetraswirlchoron is an isogonal polychoron with 24 tetragonal disphenoids, 48 phyllic disphenoids, and 16 vertices. 6 tettragonal and 12 phyllic disphenoids join at each vertex.

It is the second in an infinite family of isogonal tetrahedral swirlchora and is one of several isogonal polychora that can be formed as hulls of various combinations of 2 hexadecachora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{6+2\sqrt3}}{2}$$ ≈ 1:1.53819.

Vertex coordinates
Coordinates for the vertices of a tetrafold tetraswirlchoron of circumradius 1, centered at the origin, are:
 * $$\left(0,\,0,\,0,\,±1\right),$$
 * $$\left(0,\,0,\,±1,\,0\right),$$
 * $$±\left(0,\,\frac{\sqrt6}{3},\,\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(±\frac{\sqrt6}{3},\,0,\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$±\left(\frac{\sqrt6}{6},\,\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$±\left(\frac{\sqrt6}{6},\,-\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$±\left(\frac{\sqrt2}{2},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0\right).$$

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Edge (16): Tetrafold tetraswirlchoron
 * Edge (24): Icositetrachoron
 * Edge (48): Dodecafold tetraswirlchoron