Tetradecafold tetraswirlchoron

The tetradecafold tetraswirlchoron is an isogonal polychoron with 336 phyllic disphenoids of two kinds and 56 vertices. 24 disphenoids join at each vertex. It is the seventh in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{18-6\sqrt3\sin\frac{2\pi}{7}}}{6\sin\frac{\pi}{14}}$$ ≈ 1:2.35367.

Vertex coordinates
Coordinates for the vertices of a tetradecafold 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 6.
 * ±(0, 0, sin(kπ/7), cos(kπ/7)),
 * ±($\sqrt{6}$sin(kπ/7)/3, $\sqrt{6}$cos(kπ/7)/3, $\sqrt{3}$cos(kπ/7)/3, $\sqrt{3}$sin(kπ/7)/3),