Truncated Dodecahedron - Cartesian Coordinates

Cartesian Coordinates

The following Cartesian coordinates define the vertices of a truncated dodecahedron with edge length 2(τ−1), centered at the origin:

(0, ±1/τ, ±(2+τ))

(±(2+τ), 0, ±1/τ)

(±1/τ, ±(2+τ), 0)

(±1/τ, ±τ, ±2τ)

(±2τ, ±1/τ, ±τ)

(±τ, ±2τ, ±1/τ)

(±τ, ±2, ±τ2)

(±τ2, ±τ, ±2)

(±2, ±τ2, ±τ)

where τ = (1 + √5) / 2 is the golden ratio (also written φ).