Icositetrafold cuboctaswirlchoron

The icositetrafold cuboctaswirlchoron is an isogonal polychoron with 144 square gyroprisms, 192 triangular gyroprisms, and 288 vertices. 4 square gyroprisms and 4 triangular gyroprisms join at each vertex. 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)/$\sqrt{2}$),