Triangular double gyroantiprismoid

The triangular double gyroantiprismoid is a convex isogonal polychoron and the second member of the double gyroantiprismoid family. It consists of 12 triangular antiprisms, 18 tetragonal disphenoids, 36 rhombic disphenoids, and 72 sphenoids. 2 triangular antiprisms, 2 tetragonal disphenoids, 4 rhombic disphenoids, and 8 sphenoids join at each vertex. However, it cannot be made uniform. It is the second in an infinite family of isogonal triangular prismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{15+3\sqrt6}}{3}$$ ≈ 1:1.57581.

Vertex coordinates
The vertices of a triangular double gyroantiprismoid, assuming that the octahedra are regular of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt6}{3}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,0,\,-\frac{\sqrt6}{3}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt6}{3}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,0,\,-\frac{\sqrt6}{3}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt6}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,-\frac{\sqrt6}{3},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,\frac{\sqrt6}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt6}{3},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,\frac{\sqrt6}{6},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,\frac{\sqrt6}{6},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right).$$