Icositetrafold octaswirlchoron

The icositetrafold octaswirlchoron is an isogonal polychoron with 192 triangular antiprisms, 288 rhombic disphenoids and 144 vertices. It is the sixth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{12+6\sqrt2+4\sqrt{9+6\sqrt2}}}{2}$$ ≈ 1:3.05006.

Vertex coordinates
Coordinates for the vertices of an icositetrafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations and sign changes of: defining an icositetrachoron, along with reflections through the x=y and z=w hyperplanes and with all sign changes of: along with reflections through the x=y and z=w hyperplanes and with all even sign changes of: along with reflections through the x=y and z=w hyperplanes and with all odd sign changes of:
 * (0, 0, 0, 1),
 * (1/2, 1/2, 1/2, 1/2),
 * (0, 0, $\sqrt{2}$/2, $\sqrt{2}$/2),
 * (0, $\sqrt{2}$/2, 0, $\sqrt{2}$/2),
 * (0, $\sqrt{2}$/2, $\sqrt{2}$/2, 0),
 * (0, 0, $\sqrt{2-√3}$/2, $\sqrt{2+√3}$/2),
 * (0, 0, 1/2, $\sqrt{3}$/2),
 * (($\sqrt{3}$–1)/4, ($\sqrt{3}$+1)/4, ($\sqrt{3}$–1)/4, ($\sqrt{3}$+1)/4),
 * ($\sqrt{2}$/4, $\sqrt{6}$/4, $\sqrt{2}$/4, $\sqrt{6}$/4),
 * (($\sqrt{3}$-1)/4, ($\sqrt{3}$+1)/4, ($\sqrt{3}$+1)/4, ($\sqrt{3}$-1)/4),
 * ($\sqrt{2}$/4, $\sqrt{6}$/4, $\sqrt{6}$/4, $\sqrt{2}$/4).

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