Gyroelongated triangular bicupola

The gyroelongated triangular bicupola is one of the 92 Johnson solids (J44). It consists of 2+6+6+6 triangles and 6 squares. It can be constructed by attaching triangular cupolas to the bases of the hexagonal antiprism.

It is one of the five Johnson solids to be chiral.

Vertex coordinates
Coordinates for the vertices of a gyroelongated triangular bicupola of edge length 1 are given by:


 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,\frac{2\sqrt6+3\sqrt{\sqrt3-1}}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,\frac{2\sqrt6+3\sqrt{\sqrt3-1}}{6}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,\frac{\sqrt{\sqrt3-1}}{2}\right),$$
 * $$\left(±1,\,0,\,\frac{\sqrt{\sqrt3-1}}{2}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,-\frac{\sqrt{\sqrt3-1}}{2}\right),$$
 * $$\left(0,\,±1,\,-\frac{\sqrt{\sqrt3-1}}{2}\right),$$
 * $$\left(-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{2\sqrt6+3\sqrt{\sqrt3-1}}{6}\right),$$
 * $$\left(\frac{\sqrt3}{3},\,0,\,-\frac{2\sqrt6+3\sqrt{\sqrt3-1}}{6}\right).$$