Compound of Ten Octahedra - Cartesian Coordinates

Cartesian Coordinates

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

(0, ±(τ−1√2 + 2sτ), ±(τ√2 − 2sτ−1))

(±(√2 − sτ2), ±(√2 + s(2τ − 1)), ±(√2 + sτ−2))

(±(τ−1√2 − sτ), ±(τ√2 + sτ−1), ±3s)

where τ = (1 + √5)/2 is the golden ratio (sometimes written φ) and s is either +1 or −1. Setting s = −1 gives UC₁₅, while s = +1 gives UC₁₆.