Icositetrafold cubiswirlchoron

The icositetrafold cubiswirlchoron is an isogonal polychoron with 144 square antiprisms, 288 rhombic disphenoids and 192 vertices. It is the second in an infinite family of isogonal cubic swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{18+9\sqrt2+6\sqrt{9+6\sqrt2}}}{3}$$ ≈ 1:2.49036.

Vertex coordinates
Coordinates for the vertices of an icositetrafold cubiswirlchoron of circumradius 1, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of: where k is an integer from 0 to 11.
 * ±(sin(kπ/12)/$\sqrt{3+√3}$, cos(kπ/12)/$\sqrt{3+√3}$, cos(kπ/12)/$\sqrt{3-√3}$, sin(kπ/12)/$\sqrt{3-√3}$),
 * ±(sin(kπ/12)/$\sqrt{3-√3}$, cos(kπ/12)/$\sqrt{3-√3}$, cos(kπ/12)/$\sqrt{3+√3}$, sin(kπ/12)/$\sqrt{3+√3}$),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Square antiprism (144): Icositetrafold octaswirlchoron
 * Square (144): Icositetrafold octaswirlchoron
 * Edge (192): Icositetrafold cubiswirlchoron