Icosafold octaswirlchoron

The icosafold octaswirlchoron is an isogonal polychoron with 480 tetragonal disphenoids of two kinds, 480 phyllic disphenoids, and 120 vertices. 16 tetragonal and 16 phyllic disphenoids join at each vertex. It is the fifth in an infinite family of isogonal octahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{12+2\sqrt5+2\sqrt{25+10\sqrt5}}}{2}$$ ≈ 1:2.74936.

Vertex coordinates
Coordinates for the vertices of an icosafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations of: defining an 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:
 * $$\left(0,\,0,\,0,\,±1\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{8}}\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}}\right),$$
 * $$\left(\frac{1+\sqrt5-\sqrt{10-2\sqrt5}}{8},\,\frac{1+\sqrt5+\sqrt{10-2\sqrt5}}{8},\,\frac{1+\sqrt5-\sqrt{10-2\sqrt5}}{8},\,\frac{1+\sqrt5+\sqrt{10-2\sqrt5}}{8}\right),$$
 * $$\left((\frac{1-\sqrt5+\sqrt{10+2\sqrt5}}{8},\,\frac{\sqrt5+\sqrt{10+2\sqrt5}-1}{8},\,\frac{1-\sqrt5+\sqrt{10+2\sqrt5}}{8},\,\frac{\sqrt5+\sqrt{10+2\sqrt5}-1}{8}\right),$$
 * $$\left(\frac{1+\sqrt5-\sqrt{10-2\sqrt5}}{8},\,\frac{1+\sqrt5+\sqrt{10-2\sqrt5}}{8},\,\frac{1+\sqrt5+\sqrt{10-2\sqrt5}}{8},\,\frac{1+\sqrt5-\sqrt{10-2\sqrt5}}{8}\right),$$
 * $$\left(\frac{1-\sqrt5+\sqrt{10+2\sqrt5}}{8},\,\frac{\sqrt5+\sqrt{10+2\sqrt5}-1}{8},\,\frac{\sqrt5+\sqrt{10+2\sqrt5}-1}{8},\,\frac{1-\sqrt5+\sqrt{10+2\sqrt5}}{8}\right).$$