Tetracontafold cuboctaswirlchoron

The tetracontafold cuboctaswirlchoron is an isogonal polychoron with 240 square antiprisms, 1920 phyllic disphenoids of two kinds and 480 vertices. It is the fifth in an infinite family of isogonal cuboctahedral swirlchora.

Vertex coordinates
Coordinates for the vertices of a tetracontafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 90°, 180° and 270° rotations in the xy axis of: where k is an integer from 0 to 19.
 * ±(sin(kπ/20)/$\sqrt{4+2√2}$, cos(kπ/20)/$\sqrt{4+2√2}$, cos(kπ/20)/$\sqrt{4-2√2}$, sin(kπ/20)/$\sqrt{4-2√2}$),
 * ±(sin(kπ/20)/$\sqrt{4-2√2}$, cos(kπ/20)/$\sqrt{4-2√2}$, cos(kπ/20)/$\sqrt{4+2√2}$, sin(kπ/20)/$\sqrt{4+2√2}$),
 * ±(sin((2k+5)π/40)/$\sqrt{2}$, cos((2k+5)π/40)/$\sqrt{2}$, cos((2k-5)π/40)/$\sqrt{2}$, sin((2k-5)π/40)/$\sqrt{2}$),