Icositetrafold cuboctaswirlchoron

The icositetrafold cuboctaswirlchoron is an isogonal polychoron with 144 square antiprisms, 192 triangular antiprisms and 288 vertices. It is the third in an infinite family of isogonal cuboctahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt{5+2\sqrt6}}{2}$$ ≈ 1:2.07313.

Vertex coordinates
Coordinates for the vertices of an icositetrafold 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 11.
 * ±(sin(kπ/12)/$\sqrt{4+2√2}$, cos(kπ/12)/$\sqrt{4+2√2}$, cos(kπ/12)/$\sqrt{4-2√2}$, sin(kπ/12)/$\sqrt{4-2√2}$),
 * ±(sin(kπ/12)/$\sqrt{4-2√2}$, cos(kπ/12)/$\sqrt{4-2√2}$, cos(kπ/12)/$\sqrt{4+2√2}$, sin(kπ/12)/$\sqrt{4+2√2}$),
 * ±(sin((2k+3)π/24)/$\sqrt{2}$, cos((2k+3)π/24)/$\sqrt{2}$, cos((2k-3)π/24)/$\sqrt{2}$, sin((2k-3)π/24)/$\sqrt{2}$),