Hexadecafold octaswirlchoron

The hexadecafold octaswirlchoron is an isogonal polychoron with 192 rhombic disphenoids, 384 phyllic disphenoids, and 96 vertices. 8 rhombic and 16 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt2+4\sqrt{2+\sqrt2}}}{2}$$ ≈ 1:2.13421.

Vertex coordinates
Coordinates for the vertices of a hexadecafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations of: defining an icositetrachoron, along with all permutations of: defining a 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:
 * $$\left(0,\,0,\,0,\,±1\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2}\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt{2-\sqrt2}}{2},\,±\frac{\sqrt{2+\sqrt2}}{2}\right),$$
 * $$\left(\sqrt{\frac{2-\sqrt2}{8}},\,\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2-\sqrt2}{8}},\,\sqrt{\frac{2+\sqrt2}{8}}\right),$$
 * $$\left(\sqrt{\frac{2-\sqrt2}{8}},\,\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2-\sqrt2}{8}}\right).$$