Truncated Icosahedron - Cartesian Coordinates

Cartesian Coordinates

Cartesian coordinates for the vertices of a truncated icosahedron centered at the origin are all even permutations of:

(0, ±1, ±3φ)

(±2, ±(1+2φ), ±φ)

(±1, ±(2+φ), ±2φ)

where φ = (1 + √5) / 2 is the golden mean. Using φ2 = φ + 1 one verifies that all vertices are on a sphere, centered at the origin, with the radius squared equal to 9φ + 10. The edges have length 2.