Cartesian Coordinates
Cartesian coordinates for the vertices of a great truncated icosidodecahedron centered at the origin are all the even permutations of
- (±τ, ±τ, ±(3−1/τ)),
- (±2τ, ±1/τ, ±(1−2/τ)),
- (±τ, ±1/τ2, ±(1+3/τ)),
- (±(1+2/τ), ±2, ±(2−1/τ)) and
- (±1/τ, ±3, ±2/τ),
where τ = (1+√5)/2 is the golden ratio.
Read more about this topic: Great Truncated Icosidodecahedron