A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout's identities

Abstract

Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplanes for dimensions higher than 3. Here, a method is presented to find them. Equivalently, it gives the solutions of the N-dimensional Bézout's identity associated with the Miller indices of the hyperplane.