Truncated Great Icosahedron - Cartesian Coordinates

Cartesian Coordinates

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

(±1, 0, ±3/τ)

(±2, ±1/τ, ±1/τ3)

(±(1+1/τ2), ±1, ±2/τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ). Using 1/τ2 = 1 − 1/τ one verifies that all vertices are on a sphere, centered at the origin, with the radius squared equal to 10−9/τ. The edges have length 2.