(two-dimensional) crystallographic group
planar (or wallpaper) group is a mathematical
concept to classify repetitive (periodic) designs on two-dimensional surfaces, such as
wallpapers, based on the symmetries in the pattern. Such patterns occur frequently
in architecture and decorative art. The mathematical study of the patterns
that only 17 different types of them can occur.
Wallpaper groups are related to the more
complex three-dimensional crystallographic groups (also called space groups).