The symmetry of crystal surfaces can be classified as one of 17 possible plane
symmetry groups (also sometimes referred to as “wallpaper groups”). For more
information, see, for example, the corresponding
Wikipedia article.

These groups are defined by the shape of the unit cell and by the symmetry
operations that leave the surface invariant: rotation axes, mirror planes,
and glide planes. Fig. 2, shows an overview of the 17
plane groups, allowed symmetry operations and possible subgroups. There,
an “×” indicates the point used by ViPErLEED as the conventional position
of the origin of the unit cell. See the relevant ViPErLEED publication for
more details [3].