Octafold ambotetraswirlchoron

The octafold ambotetraswirlchoron is an isogonal polychoron with 32 triangular gyroprisms, 96 phyllic disphenoids, and 48 vertices. 4 triangular gyroprisms and 8 phyllic disphenoids join at each vertex. 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)/$\sqrt{3+√3}$),