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Figure 1
The space group [{\cal G}_{\rm C}] of a crystal is the set of all isometries that transform any point of the crystal into an equivalent one. The invariance group [{\cal N}_P] of a subset [{\cal P} \subset {\cal C}] of the atoms of a crystal is generally different from [{\cal G}_{\rm C}] and is not necessarily a subgroup of [{\cal G}_{\rm C}].

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