Icositetrafold cubiswirlchoron

The icositetrafold cubiswirlchoron is an isogonal polychoron with 144 square gyroprisms, 288 rhombic disphenoids, and 192 vertices. 6 square gyroprisms and 6 rhombic disphenoids join at each vertex. 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): where k is an integer from 0 to 11.
 * $$\left(\frac{\sin\left(k\pi/12\right)}{\sqrt{3+\sqrt3}},\,\frac{\cos\left(k\pi/12\right)}{\sqrt{3+\sqrt3}},\,\frac{\cos\left(k\pi/12\right)}{\sqrt{3-\sqrt3}},\,\frac{\sin\left(k\pi/12\right)}{\sqrt{3-\sqrt3}}\right),$$
 * $$\left(\frac{\sin\left(k\pi/12\right)}{\sqrt{3-\sqrt3}},\,\frac{\cos\left(k\pi/12\right)}{\sqrt{3-\sqrt3}},\,\frac{\cos\left(k\pi/12\right)}{\sqrt{3+\sqrt3}},\,\frac{\sin\left(k\pi/12\right)}{\sqrt{3+\sqrt3}}\right),$$

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