Tetracontafold cuboctaswirlchoron

The tetracontafold cuboctaswirlchoron is an isogonal polychoron with 240 square gyroprisms, 1920 phyllic disphenoids of two kinds, and 480 vertices. 4 square gyroprisms and 16 phyllic disphenoids join at each vertex. 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)/$\sqrt{2}$),