Icosafold octaswirlchoron

The 5-cubic swirlprism is an isogonal polychoron with 480 tetragonal disphenoids of two kinds, 480 phyllic disphenoids and 96 vertices. Together with its dual, it is the fifth in an infinite family of cubic swirlchora.

Vertex coordinates
Coordinates for the vertices of a 5-cubic swirlprism 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, ($\sqrt{5}$-1)/4, $\sqrt{10+2√5}$/4),
 * (0, 0, $\sqrt{10+2√5}$/4, ($\sqrt{5}$-1)/4),
 * (($\sqrt{5}$-1)/4, $\sqrt{10+2√5}$/4, 0, 0),
 * ($\sqrt{10+2√5}$/4, ($\sqrt{5}$-1)/4, 0, 0),
 * (0, 0, (1+$\sqrt{5}$)/4, $\sqrt{10-2√5}$/4),
 * (0, 0, $\sqrt{10-2√5}$/4, (1+$\sqrt{5}$)/4),
 * ((1+$\sqrt{5}$)/4, $\sqrt{10-2√5}$/4, 0, 0),
 * ($\sqrt{10-2√5}$/4, (1+$\sqrt{5}$)/4, 0, 0),
 * ((1+$\sqrt{5}$-$\sqrt{10-2√5}$)/8, (1+$\sqrt{5}$+$\sqrt{10-2√5}$)/8, (1+$\sqrt{5}$-$\sqrt{10-2√5}$)/8, (1+$\sqrt{5}$+$\sqrt{10-2√5}$)/8),
 * ((1-$\sqrt{5}$+$\sqrt{10+2√5}$)/8, ($\sqrt{5}$+$\sqrt{10+2√5}$-1)/8, (1-$\sqrt{5}$+$\sqrt{10+2√5}$)/8, ($\sqrt{5}$+$\sqrt{10+2√5}$-1)/8),
 * ((1+$\sqrt{5}$-$\sqrt{10-2√5}$)/8, (1+$\sqrt{5}$+$\sqrt{10-2√5}$)/8, (1+$\sqrt{5}$+$\sqrt{10-2√5}$)/8, (1+$\sqrt{5}$-$\sqrt{10-2√5}$)/8),
 * ((1-$\sqrt{5}$+$\sqrt{10+2√5}$)/8, ($\sqrt{5}$+$\sqrt{10+2√5}$-1)/8, ($\sqrt{5}$+$\sqrt{10+2√5}$-1)/8, (1-$\sqrt{5}$+$\sqrt{10+2√5}$)/8).