International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 
International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 172

In one dimension, only one crystal family, one crystal system and one Bravais lattice exist. No name or common symbol is required for any of them. All onedimensional lattices are primitive, which is symbolized by the script letter ; cf. Table 2.1.1.1.
There occur two types of onedimensional point groups, 1 and . The latter contains reflections through a point (reflection point or mirror point). This operation can also be described as inversion through a point, thus for one dimension; cf. Section 2.1.2.
Two types of line groups (onedimensional space groups) exist, with Hermann–Mauguin symbols and , which are illustrated in Fig. 2.1.3.13. Line group , which consists of onedimensional translations only, has merely one (general) position with coordinate x. Line group consists of onedimensional translations and reflections through points. It has one general and two special positions. The coordinates of the general position are x and ; the coordinate of one special position is 0, that of the other . The site symmetries of both special positions are . For , the origin is arbitrary, for it is at a reflection point.
The onedimensional point groups are of interest as `edge symmetries' of twodimensional `edge forms'; they are listed in Table 3.2.3.1 . The onedimensional space groups occur as projection and section symmetries of crystal structures.
References
International Tables for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002).]International Tables for Crystallography (2010). Vol. A1, 2nd ed., edited by H. Wondratschek & U. Müller. Chichester: Wiley. [Abbreviated as IT A1 (2010).]
International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]
Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]
Wolff, P. M. de, Belov, N. V., Bertaut, E. F., Buerger, M. J., Donnay, J. D. H., Fischer, W., Hahn, Th., Koptsik, V. A., Mackay, A. L., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1985). Nomenclature for crystal families, Bravaislattice types and arithmetic classes. Report of the International Union of Crystallography Adhoc Committee on the Nomenclature of Symmetry. Acta Cryst. A41, 278–280.