Line group

A line group is a mathematical way of describing symmetries associated with moving along a line. These symmetries may include repeating along that line, making that line a one-dimensional lattice. Most line groups have more than one dimension, and involve those dimensions in its isometries or symmetry transformations.

One constructs a line group by taking a point group in the full dimensions of the space and adding translations (sometimes with a twist) along the line to each of the point group's elements, in the fashion of constructing a space group. Although a point group by definition holds at least one point stationary, this is not necessarily true of a line group because of the translations.

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