Z4

Z4 is a non-convex regular faced polyhedron. Although it is spherical, it is used for tunneling many Stewart toroids.

Vertex coordinates
The vertex coordinates for Z4 with unit side length are:


 * $$\left(\pm\frac12,\pm\frac12,\pm\frac{1+\sqrt{5}}4\right)$$,
 * $$\left(\pm\frac{1+\sqrt{5}}4,0,0\right)$$,

and all even sign changes of:


 * $$\left(0,\pm\frac{5+3\sqrt{5}}{20},\pm\frac{2\sqrt{5}-5}{10}\right)$$,
 * $$\left(0,\pm\frac{\sqrt{5}-1}{4},\pm\frac12\right)$$.