Minimal enclosing parallelepiped in 3D

We investigate the problem of finding a minimal volume parallelepiped enclosing a given set of n three-dimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n⁶). Experiments show that in practice our quickest algorithm runs in O(n²) (at least for n10⁵). We also present our application in structural biology.