A frieze group is a discrete symmetry group of the Euclidean plane whose translations are generated by a single nonzero translation. Such a group describes the symmetries of a pattern that repeats indefinitely in one direction, as on an infinite strip.
Besides translations, the symmetries in a frieze group can include half-turns, reflections
in lines parallel or perpendicular
to the direction of translation, and glide reflections
(also called glides). The compatibility conditions among
these symmetries give exactly seven frieze groups (Conway and Huson 2002). In orbifold
notation, they are 
,
, 
, 
, 
, 
, and 
. The last of these contains translations
only, while 
contains reflection axes in both directions and half-turns.
Frieze groups are the one-periodic analogs of the wallpaper groups, which contain independent translations in two directions.
