In the context of chemistry and crystallography, a point group is a set of symmetry operations that describe the symmetrical properties of a particular molecule or crystal structure. These operations include rotations, reflections, and inversions that leave at least one point (usually the center of the molecule or crystal) unchanged.
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The point group of a Euclidean crystallographic group is the group of its orthogonal linear parts, equivalently its quotient by the translation subgroup. It preserves the translation Euclidean lattice. In an arbitrary dimension it is a finite orthogonal group; for a plane crystallographic group this lattice preservation restricts the allowed rotation orders.
