Hexagonal double gyroantiprismoid

The hexagonal double gyroantiprismoid is a convex isogonal polychoron and the third member of the double gyroantiprismoids that consists of 24 hexagonal antiprisms, 72 tetragonal disphenoids, 144 rhombic disphenoids and 288 sphenoids. 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:
 * (0, ±1, 0, ±$\sqrt{1+√3}$),
 * (0, ±1, ±$\sqrt{3+3√3}$/2, ±$\sqrt{1+√3}$/2),
 * (±$\sqrt{3}$/2, ±1/2, 0, ±$\sqrt{1+√3}$),
 * (±$\sqrt{3}$/2, ±1/2, ±$\sqrt{3+3√3}$/2, ±$\sqrt{1+√3}$/2),
 * (±1, 0, ±$\sqrt{1+√3}$, 0),
 * (±1, 0, ±$\sqrt{1+√3}$/2, ±$\sqrt{3+3√3}$/2),
 * (±1/2, ±$\sqrt{3}$/2, ±$\sqrt{1+√3}$, 0),
 * (±1/2, ±$\sqrt{3}$/2, ±$\sqrt{1+√3}$/2, ±$\sqrt{3+3√3}$/2),
 * (0, ±$\sqrt{1+√3}$, 0, ±1),
 * (0, ±$\sqrt{1+√3}$, ±$\sqrt{3}$/2, ±1/2),
 * (±$\sqrt{3+3√3}$/2, ±$\sqrt{1+√3}$/2, 0, ±1),
 * (±$\sqrt{3+3√3}$/2, ±$\sqrt{1+√3}$/2, ±$\sqrt{3}$/2, ±1/2),
 * (±$\sqrt{1+√3}$, 0, ±1, 0),
 * (±$\sqrt{1+√3}$, 0, ±1/2, ±$\sqrt{3}$/2),
 * (±$\sqrt{1+√3}$/2, ±$\sqrt{3+3√3}$/2, ±1, 0),
 * (±$\sqrt{1+√3}$/2, ±$\sqrt{3+3√3}$/2, ±1/2, ±$\sqrt{3}$/2).