A frieze pattern is a planar pattern that is repeating in one direction. As such they are common in decorations and architecture. Formally a frieze pattern is such that its group of symmetries—called a frieze group—has a subgroup of translations that is isomorphic to the integers.

An example of a frieze pattern

The frieze group of the pattern in the figure is generated by x, a translation two tiles to the right, and y, a half-turn, and is isomorphic to

and its subgroup of translations is ⟨x⟩. It can be shown that, up to isomorphism, there are seven frieze groups. Compare crystallographic groups.