Gyroelongated square bicupola

The gyroelongated square bicupola is one of the 92 Johnson solids (J45). It consists of 8+8+8 triangles and 2+8 squares. It can be constructed by attaching square cupolas to the bases of the octagonal antiprism.

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

Vertex coordinates
A gyroelongated square bicupola of edge length 1 has the following vertices:
 * $$\left(±\frac12,\,±\frac12,\,\frac{\sqrt2+2H}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,H\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,H\right),$$
 * $$\left(0,\,±\sqrt{\frac{2+\sqrt2}2},\,-H\right),$$
 * $$\left(±\sqrt{\frac{2+\sqrt2}2},\,0,\,-H\right),$$
 * $$\left(±\frac{\sqrt{2+\sqrt2}}2,\,±\frac{\sqrt{2+\sqrt2}}2,\,-H\right),$$
 * $$\left(\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2-\sqrt2}{8}},\,-\frac{\sqrt2+2H}{2}\right),$$
 * $$\left(-\sqrt{\frac{2+\sqrt2}{8}},\,-\sqrt{\frac{2-\sqrt2}{8}},\,-\frac{\sqrt2+2H}{2}\right),$$
 * $$\left(-\sqrt{\frac{2-\sqrt2}{8}},\,\sqrt{\frac{2+\sqrt2}{8}},\,-\frac{\sqrt2+2H}{2}\right),$$
 * $$\left(\sqrt{\frac{2-\sqrt2}{8}},\,-\sqrt{\frac{2+\sqrt2}{8}},\,-\frac{\sqrt2+2H}{2}\right),$$

where $$H=\sqrt{\frac{-2-2\sqrt2+\sqrt{20+14\sqrt2}}{8}}$$ is the distance between the octagonal antiprism's center and the center of one of its bases.