Dodecafold triantiprismatoswirlchoron

The dodecafold triantiprismatoswirlchoron is an isogonal polychoron with 24 triangular antiprisms, 144 phyllic disphenoids of two kinds, 144 irregular tetrahedra and 72 vertices. It is the second in an infinite family of isogonal triangular antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{14+7\sqrt3-\sqrt{119+68\sqrt3}}}{2}$$ ≈ 1:1.63835.

Vertex coordinates
Coordinates for the vertices of a dodecafold triantiprismatoswirlchoron, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of: where a = $\sqrt{3}$/3, b = $\sqrt{78+18√17}$/12 and k is an integer from 0 to 5.
 * ±(a*sin(kπ/6), a*cos(kπ/6), b*cos(kπ/6), b*sin(kπ/6)),
 * ±(b*sin((k+2)π/6), b*cos((k+2)π/6), a*cos(kπ/6), a*sin(kπ/6)),