Point Groups
A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the requirement that symmetry be present in a lattice requires that only 1, 2, 3, 4, and 6-fold symmetry axes are possible (the crystallography restriction), which restricts the number of possible so-called crystallographic point groups to 32.
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point groups
