a1ab12unit meshes (unit nets)

ssss1 The 10 plane point groups defined by rotational and reflection symmetry.

Source: Klein and Hurlbut (1985). © John Wiley & Sons.

Square unit meshesabPrimitive rectangular unit meshesabDiamond unit meshesprimitive diamond unit meshesabcentered rectangular unit meshesabhexagonal unit meshabOblique unit meshesab

17 plane lattice groups

ssss1 The five principal types of meshes or nets and their unit meshes (shaded gray): (a) square, (b) primitive rectangle, (c) diamond or centered rectangle, (d) hexagonal, (e) oblique.

Source: Nesse (2016). © Oxford University Press.

ssss1 The 17 plane lattice groups and the unique combination of point group and unit mesh that characterizes each.

Lattice Point group Plane group Oblique (P) 1 P1 2 P2 Rectangular (P and C) m Pm Pg Cm 2mm P2mm P2mg P2gg C2mm Square (P) 4 P4 4mm P4mm P4gm Hexagonal (P) (rhombohedral) 3 P3 3m P3m1 P3lm Hexagonal (P) (hexagonal) 6 P6 6mm P6mm

The details of plane lattice groups are well documented (see for example, Klein and Dutrow 2007), but are beyond the introductory material in this text.