International
Tables for Crystallography Volume E Subperiodic groups Edited by V. Kopský and D. B. Litvin © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. E, ch. 1.2, pp. 1617
Section 1.2.14. Symmetry of special projections^{a}Department of Physics, University of the South Pacific, Suva, Fiji, and Institute of Physics, The Academy of Sciences of the Czech Republic, Na Slovance 2, PO Box 24, 180 40 Prague 8, Czech Republic, and ^{b}Department of Physics, Penn State Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 196106009, USA 
Under the heading Symmetry of special projections, the following data are listed for three orthogonal projections of each layer group and rod group and two orthogonal projections of each frieze group:

The only centred subperiodic groups are the nine types of centred layer groups. For the [100] and [010] projection directions, because of the centred layergroup lattice, the basis vectors of the resulting frieze groups are a′ = b/2 and a′ = a/2, respectively.
A symmetry element of a subperiodic group projects as a symmetry element only if its orientation bears a special relationship to the projection direction. In Table 1.2.14.2, the threedimensional symmetry elements of the layer and rod groups and in Table 1.2.14.3 the twodimensional symmetry elements of the frieze groups are listed along with the corresponding symmetry element in projection.
^{†}The term `with ⊥ component' refers to the component of the glide vector normal to the projection direction.


Example: Layer group cm2m (L35)
Projection along [001]: This orthorhombic/rectangular plane group is centred; m perpendicular to [100] is projected as a reflection line, 2 parallel to [010] is projected as the same reflection line and m perpendicular to [001] gives rise to no symmetry element in projection, but to an overlap of atoms. Result: Plane group c1m1 (5) with a′ = a and b′ = b.
Projection along [100]: The frieze group has the basis vector a′ = b/2 due to the centred lattice of the layer group. m perpendicular to [100] gives rise only to an overlap of atoms, 2 parallel to [010] is projected as a reflection line and m perpendicular to [001] is projected as the same reflection line. Result: Frieze group (F4) with a′ = b/2.
Projection along [010]: The frieze group has the basis vector a′ = a/2 due to the centred lattice of the layer group. The two reflection planes project as perpendicular reflection lines and 2 parallel to [010] projects as the rotation point 2. Result: Frieze group (F6) with a′ = a/2.