Octafold ambotetraswirlchoron

The octafold ambotetraswirlchoron is an isogonal polychoron with 32 triangular antiprisms, 96 phyllic disphenoids and 24 vertices. It is the second in an infinite family of isogonal ambotetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+4\sqrt2-2\sqrt{9+6\sqrt2}}}{2}$$ ≈ 1:1.15041.

Vertex coordinates
Coordinates for the vertices of an octafold ambotetraswirlchoron of circumradius 1, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of: where k is an integer from 0 to 3.
 * ±(sin(kπ/4)/$\sqrt{3+√3}$, cos(kπ/4)/$\sqrt{3+√3}$, cos(kπ/4)/$\sqrt{3-√3}$, sin(kπ/4)/$\sqrt{3-√3}$),
 * ±(sin((k+1)π/4)/$\sqrt{3-√3}$, cos((k+1)π/4)/$\sqrt{3-√3}$, -cos((k+1)π/4)/$\sqrt{3+√3}$, -sin((k+1)π/4)/$\sqrt{3+√3}$),