Chiroicosafold cuboctaswirlchoron

The chiroicosafold cuboctaswirlchoron is an isogonal polychoron with 240 rhombic disphenoids, 1440 phyllic disphenoids of three kinds, and 240 vertices. 4 rhombic disphenoids and 24 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal chiral cuboctahedral swirlchora.

Vertex coordinates
Coordinates for the vertices of a chiroicosafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 180° rotations in the xy axis and even sign changes of the first and third coordinates of:: where k is an integer from 0 to 9.
 * ±(sin(kπ/10)/$\sqrt{4+2√2}$, cos(kπ/10)/$\sqrt{4+2√2}$, cos(kπ/10)/$\sqrt{4-2√2}$, sin(kπ/10)/$\sqrt{4-2√2}$),
 * ±(sin(kπ/10)/$\sqrt{4-2√2}$, cos(kπ/10)/$\sqrt{4-2√2}$, cos(kπ/10)/$\sqrt{4+2√2}$, sin(kπ/10)/$\sqrt{4+2√2}$),
 * ±(cos((2k-1)π/20)/$\sqrt{4+2√2}$, -sin((2k-1)π/20)/$\sqrt{4+2√2}$, cos((2k-1)π/20)/$\sqrt{4-2√2}$, sin((2k-1)π/20)/$\sqrt{4-2√2}$),
 * ±(cos((2k-1)π/20)/$\sqrt{4-2√2}$, -sin((2k-1)π/20)/$\sqrt{4-2√2}$, cos((2k-1)π/20)/$\sqrt{4+2√2}$, sin((2k-1)π/20)/$\sqrt{4+2√2}$),
 * ±(sin((4k+7)π/40)/$\sqrt{2}$, cos((4k+7)π/40)/$\sqrt{2}$, cos((4k-7)π/40)/$\sqrt{2}$, sin((4k-7)π/40)/$\sqrt{2}$),