Cartesian Coordinates
The following Cartesian coordinates define the vertices of a dodecahedron centered at the origin and suitably scaled and oriented:
- (±1, ±1, ±1)
- (0, ±1/φ, ±φ)
- (±1/φ, ±φ, 0)
- (±φ, 0, ±1/φ)
where φ = (1 + √5) / 2 is the golden ratio (also written τ) ≈ 1.618. The edge length is 2/φ = √5 – 1. The containing sphere has a radius of √3.
Read more about this topic: Dodecahedron