Hexadecafold ambotetraswirlchoron

The hexadecafold ambotetraswirlchoron is an isogonal polychoron with 64 triangular gyroprisms, 384 phyllic disphenoids of two kinds, and 96 vertices. 4 triangular gyroprisms and 16 phyllic disphenoids join at each vertex. It is the fourth in an infinite family of isogonal ambotetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{4-\sqrt6}{4-2\sqrt{2+\sqrt2}}}$$ ≈ 1:2.25661.

Vertex coordinates
Coordinates for the vertices of a hexadecafold 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 7.
 * ±(sin(kπ/8)/$\sqrt{3+√3}$, cos(kπ/8)/$\sqrt{3+√3}$, cos(kπ/8)/$\sqrt{3-√3}$, sin(kπ/8)/$\sqrt{3-√3}$),
 * ±(sin((k+1)π/8)/$\sqrt{3-√3}$, cos((k+1)π/8)/$\sqrt{3-√3}$, -cos((k+1)π/8)/$\sqrt{3+√3}$, -sin((k+1)π/8)/$\sqrt{3+√3}$),