Hexagonal double gyroantiprismoid

The hexagonal double gyroantiprismoid is a convex isogonal polychoron and the third member of the double gyroantiprismoid family. It consists of 24 hexagonal antiprisms, 72 tetragonal disphenoids, 144 rhombic disphenoids, and 288 sphenoids. 2 hexagonal 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 hexagonal prismatic swirlchora.

Vertex coordinates
The vertices of a hexagonal double gyroantiprismoid, assuming that the hexagonal antiprisms are regular of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±1,\,0,\,±\sqrt{1+\sqrt3}\right),$$
 * $$\left(0,\,±1,\,±\frac{\sqrt{3+3\sqrt3}}{2},\,±\frac{\sqrt{1+\sqrt3}}{2}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±\sqrt{1+\sqrt3}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt{3+3\sqrt3}}{2},\,±\frac{\sqrt{1+\sqt3}}{2}\right),$$
 * $$\left(±1,\,0,\,±\sqrt{1+\sqrt3},\,0\right),$$
 * $$\left(±1,\,0,\,±\frac{\sqrt{1+\sqrt3}}{2},\,±\frac{\sqrt{3+3\sqrt3}}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\sqrt{1+\sqrt3},\,0\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac{\sqrt{1+\sqrt3}}{2},\,±\frac{\sqrt{3+3\sqrt3}}{2}\right),$$
 * $$\left(0,\,±\sqrt{1+\sqrt3},\,0,\,±1\right),$$
 * $$\left(0,\,±\sqrt{1+\sqrt3},\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{3+3\sqrt3}}{2},\,±\frac{\sqrt{1+\sqrt3}}{2},\,0,\,±1\right),$$
 * $$\left(±\frac{\sqrt{3+3\sqrt3}}{2},\,±\frac{\sqrt{1+\sqrt3}}{2},\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\sqrt{1+\sqrt3},\,0,\,±1,\,0\right),$$
 * $$\left(±\sqrt{1+\sqrt3},\,0,\,±\frac12,\,±\frac{\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt{1+\sqrt3}}{2},\,±\frac{\sqrt{3+3\sqrt3}}{2},\,±1,\,0\right),$$
 * $$\left(±\frac{\sqrt{1+\sqrt3}}{2},\,±\frac{\sqrt{3+3\sqrt3}}{2},\,±\frac12,\,±\frac{\sqrt3}{2}\right).$$