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The eigensymmetry, or inherent symmetry, of a crystal is the point group or space group of a crystal, irrespective of its orientation and location in space. For instance, all individuals of a twinned crystal have the same (or the enantiomorphic) eigensymmetry but may exhibit different orientations. The orientations of each of two twin components are related by a twin operation which cannot be part of the eigensymmetry.
In morphology, the eigensymmetry is the full symmetry of a crystalline form, considered as a polyhedron by itself. The eigensymmetry point group is either the generating point group itself or a supergroup of it.
Chapter 10.1 of International Tables of Crystallography, Volume A
Chapter 3.3 of International Tables of Crystallography, Volume D