Bilinski dodecahedron

The Bilinski dodecahedron is a polyhedron with twelve golden rhombus faces. It is topologically equivalent to the rhombic dodecahedron. It is one of the five golden isozonohedra.

Vertex coordinates
The vertex coordinates of a Bilinski dodecahedron are given by:
 * $$\left(\pm\sqrt{\frac{5+\sqrt5}{10}},\,\pm\sqrt{\frac{5+\sqrt5}{10}},\,0\right),$$
 * $$\left(0,\,\pm\sqrt{\frac{5-\sqrt5}{10}},\,\pm\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(\pm\sqrt{\frac{5+\sqrt5}{10}},\,0,\,\pm\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(0,\,\pm\sqrt{\frac{5+2\sqrt5}{5}},\,0\right).$$