Hexafold pyritocubiswirlchoron

The hexafold pyritocubiswirlchoron is an isogonal polychoron with 216 rhombic disphenoids of two kinds, 144 phyllic disphenoids, and 48 vertices. It is the first in an infinite family of isogonal pyritohedral cubic swirlchora and is one of several isogonal polychora that can be formed as hulls of various combinations of 2 icositetrachora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt6}}{2}$$ ≈ 1:1.79576.

Vertex coordinates
Coordinates for the vertices of a hexafold pyritocubiswirlchoron of circumradius 1, centered at the origin, are: along with 120° and 240° rotations in the xy axis of: where k is an integer from 0 to 2.
 * ±(0, 0, sin(kπ/3), cos(kπ/3)),
 * ±(sin(kπ/3), cos(kπ/3), 0, 0),
 * ±($\sqrt{6}$sin(kπ/3)/3, $\sqrt{6}$cos(kπ/3)/3, $\sqrt{3}$cos(kπ/3)/3, $\sqrt{3}$sin(kπ/3)/3),
 * ±($\sqrt{3}$cos(kπ/3)/3, $\sqrt{3}$sin(kπ/3)/3, -$\sqrt{6}$sin(kπ/3)/3, -$\sqrt{6}$cos(kπ/3)/3),