**Synopsis**: Extended crystallographic groups, which may include hyperbolic rotations as well, are defined in terms of a faithful integral representation of a permutation group of atomic positions. This formulation unifies in a general frame the crystallographic characterization of periodic and aperiodic crystals and even of some single molecules.

**Abstract**: The definition of an extended crystallographic group is given, based on an n-dimensional Euclidean space, carrier of a faithful integral representation of a permutation group of atomic positions. The Euclidean crystallography of normal crystals and the higher-dimensional one applied to incommensurately modulated crystals, intergrowth crystals and quasicrystals are special cases of a general crystallography. The same is true for the multimetrical crystallographic characterization of ice and of snow crystals. This approach can also be applied to single molecules, leading to what may be denoted as molecular crystallography. It possibly allows non-trivial structural relations between atomic positions belonging to the asymmetric unit of the molecular point group to be obtained. Two simple molecules, polycyclic aromatic hydrocarbons, are treated as illustrative examples.

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