International
Tables for Crystallography Volume A Spacegroup symmetry Edited by Th. Hahn © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. A, ch. 4.2, p. 61
https://doi.org/10.1107/97809553602060000508 Chapter 4.2. Symbols for plane groups (twodimensional space groups) 
Comparative tables for the 17 plane groups first appeared in IT (1952). The classification of plane groups is discussed in Chapter 2.1 . Table 4.2.1.1 lists for each plane group its system, lattice symbol, point group and the planegroup number, followed by the short, full and extended Hermann–Mauguin symbols. Short symbols are included only where different from the full symbols. The next column contains the full symbol for another setting which corresponds to an interchange of the basis vectors a and b; it is only needed for the rectangular system. Multiple cells c and h for the square and the hexagonal system are introduced in the last column.

`Additional symmetry' elements are
The c cell in the square system is defined as follows: with `centring points' at 0, 0; . It plays the same role as the threedimensional C cell in the tetragonal system (cf. Section 4.3.4 ).
Likewise, the triple cell h in the hexagonal system is defined as follows: with `centring points' at 0, 0; . It is the twodimensional analogue of the threedimensional H cell (cf. Chapter 1.2 and Section 4.3.5 ).
The following example illustrates the usefulness of multiple cells.
Example: p3m1 (14)
The symbol of this plane group, described by the triple cell h, is h31m, where the symmetry elements of the secondary and tertiary positions are interchanged. `Decentring' the h cell gives rise to maximal nonisomorphic k subgroups p31m of index [3], with lattice parameters (cf. Section 4.3.5 ).