Tetrafold ambotetraswirlchoron

The tetrafold ambotetraswirlchoron is an isogonal polychoron with 16 triangular gyroprisms, 48 phyllic disphenoids, and 24 vertices. 4 triangular gyroprisms and 8 phyllic disphenoids join at each vertex. It is the first in an infinite family of isogonal ambotetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{6+2\sqrt3}{3}}$$ ≈ 1:1.77615.

Vertex coordinates
Coordinates for the vertices of a tetrafold 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 1.
 * ±(sin(kπ/2)/$\sqrt{3+√3}$, cos(kπ/2)/$\sqrt{3+√3}$, cos(kπ/2)/$\sqrt{3-√3}$, sin(kπ/2)/$\sqrt{3-√3}$),
 * ±(sin((k+1/2)π/2)/$\sqrt{3-√3}$, cos((k+1/2)π/2)/$\sqrt{3-√3}$, -cos((k+1/2)π/2)/$\sqrt{3+√3}$, -sin((k+1/2)π/2)/$\sqrt{3+√3}$),