Compound of Twenty Octahedra With Rotational Freedom - Cartesian Coordinates

Cartesian Coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±2(√3)sinθ, ±(τ−1√2+2τcosθ), ±(τ√2−2τ−1cosθ))

(±(√2−τ2cosθ+τ−1(√3)sinθ), ±(√2+(2τ−1)cosθ+(√3)sinθ), ±(√2+τ−2cosθ−τ(√3)sinθ))

(±(τ−1√2−τcosθ−τ(√3)sinθ), ±(τ√2+τ−1cosθ+τ−1(√3)sinθ), ±(3cosθ−(√3)sinθ))

(±(−τ−1√2+τcosθ−τ(√3)sinθ), ±(τ√2+τ−1cosθ−τ−1(√3)sinθ), ±(3cosθ+(√3)sinθ))

(±(−√2+τ2cosθ+τ−1(√3)sinθ), ±(√2+(2τ−1)cosθ−(√3)sinθ), ±(√2+τ−2cosθ+τ(√3)sinθ))

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