## line repetition groups

https://doi.org/10.1351/goldbook.L03564
The possible symmetries of arrays extending in one direction with a fixed @I00954@. @L03556@ 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 @I03146@ 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 @H02769@ coincides with the chain axis. In the latter case, the symbol is $$\text{s}\left(A*M/N\right)$$, where $$\text{s}$$ stands for the screw axis, $$A$$ is the class of the @H02769@, * 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 @H02769@ may also be simply denoted as $$\text{s}\left(M/N\right)$$.
Source:
Purple Book, 1st ed., p. 79 [Terms] [Book]