Triangular double chiroantiprismoid

The triangular double chiroantiprismoid is a convex isogonal polychoron and the second member of the double chiroantiprismoids that consists of 12 triangular antiprisms, 72 phyllic disphenoids of two kinds, and 72 irregular tetrahedra. 2 triangular antiprisms, 8 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{54+6\sqrt{15}}}{6}$$ ≈ 1:1.46475.

Vertex coordinates
The vertices of a triangular double chiroantiprismoid, assuming that the edge length differences are minimized using the ratio method, centered at the origin, are given by:
 * $$±\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{3+\sqrt{15}}{6}\right),$$
 * $$±\left(0,\,\frac{\sqrt3}{3},\,±\frac{\sqrt3+\sqrt5}{4},\,-\frac{3+\sqrt{15}}{12}\right),$$
 * $$±\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{3+\sqrt{15}}{6}\right),$$
 * $$±\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{\sqrt3+\sqrt5}{4},\,-\frac{3+\sqrt{15}}{2}\right),$$
 * $$±\left(\frac{3+\sqrt{15}}{6},\,0,\,\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{3+\sqrt{15}}{6},\,0,\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$±\left(-\frac{3+\sqrt{15}}{12},\,±\frac{\sqrt3+\sqrt5}{4},\,\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(-\frac{3+\sqrt{15}}{12},\,±\frac{\sqrt3+\sqrt5}{4},\,-\frac{\sqrt3}{6},\,±\frac12\right).$$