Dodecahedron

The dodecahedron is one of the five Platonic solids. It has 12 pentagons as faces, joining 3 to a vertex.

Vertex coordinates
The vertices of a cube of edge length 1, centered at the origin, are all sign changes of (±(1+$\sqrt{5}$/4, ±(1+$\sqrt{3}$)/4, ±(1+$\sqrt{15}$)/4), along with all even permutations and all sign changes of (±(3+$\sqrt{5}$)/4, ±1/2, 0).