Hexadecafold octaswirlchoron

The hexadecafold octaswirlchoron is an isogonal polychoron with 192 tetragonal disphenoids, 384 phyllic disphenoids and 96 vertices. It is the fourth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt2+5\sqrt{2+\sqrt2}}}{2}$$ ≈ 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 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, $\sqrt{2-√2}$/2, $\sqrt{2+√2}$/2),
 * ($\sqrt{4-2√2}$/4, $\sqrt{4+2√2}$/4, $\sqrt{4-2√2}$/4, $\sqrt{4+2√2}$/4),
 * ($\sqrt{4-2√2}$/4, $\sqrt{4+2√2}$/4, $\sqrt{4+2√2}$/4, $\sqrt{4-2√2}$/4).