Icositetrafold octaswirlchoron

The icositetrafold octaswirlchoron is an isogonal polychoron with 192 triangular gyroprisms, 288 rhombic disphenoids, and 144 vertices. 8 triangular gyroprisms and 8 rhombic disphenoids join at each vertex. 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 of: defining an icositetrachoron, along with all permutations of: defining the dual icositetrachoron, along with reflections through the x=y and z=w hyperplanes 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:
 * $$\left(0,\,0,\,0,\,±1\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt6-\sqrt2}{4},\,±\frac{\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(0,\,0,\,±\frac12,\,±\frac{\sqrt3}{2}\right),$$
 * $$\left(\frac{\sqrt3-1}{4},\,\frac{1+\sqrt3}{4},\,\frac{\sqrt3-1}{4},\,\frac{1+\sqrt3}{4}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt6}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt6}{4}\right),$$
 * $$\left(\frac{\sqrt3-1}{4},\,\frac{1+\sqrt3}{4},\,\frac{1+\sqrt3}{4},\,\frac{\sqrt3-1}{4}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt6}{4},\,\frac{\sqrt6}{4},\,\frac{\sqrt2}{4}\right).$$

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