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. 2.2, pp. 3335
Section 2.2.14. Symmetry of special projections^{a}Institut für Kristallographie, RheinischWestfälische Technische Hochschule, Aachen, Germany, and ^{b}Laboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands 
Projections of crystal structures are used by crystallographers in special cases. Use of socalled `twodimensional data' (zerolayer intensities) results in the projection of a crystal structure along the normal to the reciprocallattice net.
Even though the projection of a finite object along any direction may be useful, the projection of a periodic object such as a crystal structure is only sensible along a rational lattice direction (lattice row). Projection along a nonrational direction results in a constant density in at least one direction.
Under the heading Symmetry of special projections, the following data are listed for three projections of each space group; no projection data are given for the plane groups.

For centred lattices, two different cases may occur:
A symmetry element of a space group does not project as a symmetry element unless its orientation bears a special relation to the projection direction; all translation components of a symmetry operation along the projection direction vanish, whereas those perpendicular to the projection direction (i.e. parallel to the plane of projection) may be retained. This is summarized in Table 2.2.14.2 for the various crystallographic symmetry elements. From this table the following conclusions can be drawn:

Example: (15, b unique, cell choice 1)
The Ccentred cell has lattice points at 0, 0, 0 and . In all projections, the centre projects as a twofold rotation point.
Projection along [001]: The plane cell is centred; projects as m; the glide component of glide plane c vanishes and thus c projects as m.
Result: Plane group c2mm (9), .
Projection along [100]: The periodicity along b is halved because of the C centring; projects as m; the glide component of glide plane c is retained and thus c projects as g.
Result: Plane group p2gm (7), .
Projection along [010]: The periodicity along a is halved because of the C centring; that along c is halved owing to the glide component of glide plane c; projects as 2.
Result: Plane group p2 (2), .
Further details about the geometry of projections can be found in publications by Buerger (1965) and Biedl (1966).
References
Biedl, A. W. (1966). The projection of a crystal structure. Z. Kristallogr. 123, 21–26.Buerger, M. J. (1965). The geometry of projections. Tschermaks Mineral. Petrogr. Mitt. 10, 595–607.