Term: line repetition groups
https://doi.org/10.1351/goldbook.L03564

Definition:
The possible symmetries of arrays extending in one direction with a fixed repeating distance. linear polymer chains in the crystalline state must belong to one of the line repetition groups. Permitted symmetry elements are: the identity operation (symbol l); the translation along the chain axis (symbol t); the mirror plane orthogonal to the chain axis (symbol m) and that containing the chain axis (symbol d); the glide plane containing the chain axis (symbol c); the inversion centre, placed on the chain axis (symbol i); the two-fold axis orthogonal to the chain axis (symbol 2); the helical, or screw, symmetry where the axis of the helix coincides with the chain axis. In the latter case, the symbol is s A * M / N, where s stands for the screw axis, A is the class of the helix, * and / are separators, and M is the integral number of residues contained in N turns, corresponding to the identity period (M and N must be prime to each other). The class index A may be dropped if deemed unnecessary, so that the helix may also be simply denoted as s M / N.

Related Terms:
1) repeating distance (<em>of a polymer</em>) (http://doi.org/10.1351/goldbook.I00954).
2) linear polymer (<em>of a polymer</em>) (http://doi.org/10.1351/goldbook.L03556).
3) inversion (<em>of a polymer</em>) (http://doi.org/10.1351/goldbook.I03146).
4) helix (<em>of a polymer</em>) (http://doi.org/10.1351/goldbook.H02769).

Source: Purple Book, 1st ed., p. 79 (http://old.iupac.org/publications/books/author/metanomski.html)

Citation: 'line repetition groups' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.L03564

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