International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.1, p. 710

Figure 3.1.3.1 

P. M. de Wolffc
[Figure 3.1.3.1]
Figure 3.1.3.1

The net of lattice points in the plane of the reduced basis vectors a and b; OBAD is a primitive mesh. The actual choice of a and b depends on the position of the point P, which is the projection of the point [P_{0}] in the next layer (supposed to lie above the paper, thin dashed lines) closest to O. Hence, P is confined to the Voronoi domain (dashed hexagon) around O. For a given interlayer distance, P defines the complete lattice. In that sense, P and [P'] represent identical lattices; so do Q, [Q'] and [Q''], and also R and [R']. When P lies in a region marked [-c^{\rm II}] (hatched), the reduced type-II basis is formed by [{\bf a}^{\rm II}], [{\bf b}^{\rm II}] and [{\bf c} = -\overrightarrow{OP}_{0}]. Regions marked [c^{\rm I}] (cross-hatched) have the reduced type-I basis [{\bf a}^{\rm I},{\bf b}^{\rm I}] and [{\bf c} = + \overrightarrow{OP}_{0}]. Small circles in O, M etc. indicate twofold rotation points lying on the region borders (see text).