According to the crystallographic restriction it may only contain one-, two-, three-, four- and sixfold rotations or rotoinversions.
These 32 groups are one-and-the-same as the 32 types of morphological (external) crystalline symmetries derived in 1830 by Johann Friedrich Christian Hessel from a consideration of observed crystal forms.
The point group of a crystal determines, among other things, the directional variation of physical properties that arise from its structure, including optical properties such as birefringency, or electro-optical features such as the Pockels effect.
In Schoenflies notation, point groups are denoted by a letter symbol with a subscript.
The symbols used in crystallography mean the following: Due to the crystallographic restriction theorem, n = 1, 2, 3, 4, or 6 in 2- or 3-dimensional space.