Plesiotwins are oriented crystal associations based on a coincidence-site lattice (CSL) usually larger than that typical of twins. They correspond to twins by parallel hemitropy with – usually – a larger twin index. The individuals are mapped onto each other by a twofold rotation about a direction contained in the composition plane. The relative orientation of the individuals can be expressed through a rotation φ about the direction perpendicular to the composition plane. Depending on whether φ is crystallographic or not, the result is a twin or a plesiotwin. φ depends nevertheless on the choice of the reference direction in the composition plane, which is taken along one of the symmetry directions in that plane. However, when the holohedral layer group of the composition plane is p 2/ m , the choice of the reference direction is not unique and for small indices this may sometimes introduce some ambiguities in the differentiation between twins and plesiotwins. The plesiotwin lattice is the sublattice defined by the lattice nodes common to the plesiotwinned individuals; it is based on a 2D CSL in the composition plane which may or may not extend to the 3D space. We present an algorithm to compute and characterize the plesiotwin lattice based on the orthonormalization of the basis of the individual crystals, which is applicable to the study of CSLs as well. The algorithm is implemented through software described in a companion article Nespolo (2026). J. Appl. Cryst. 59 , https://doi.org/10.1107/S1600576726001147.
Massimo NESPOLO (Thu,) studied this question.