Cartesian Coordinates
The coordinates of the 8 vertices:
- (±1, ±1, ±1)
The coordinates of the 12 vertices are the permutations of:
- (0, 1+h, 1−h2)
where h is the height of the wedge roof above the faces of the cube. When h=1, the 6 edges degenerate to points and rhombic dodecahedron is formed. For the regular dodecahedron, h=(√5−1)/2, the golden ratio.
Read more about this topic: Pyritohedron