Frieze groups are mathematical classifications that describe patterns in two-dimensional space, particularly those that repeat in one direction. They are used to analyze the symmetries of friezes, which are decorative borders or bands found in art and architecture. There are seven distinct frieze groups, each defined by specific symmetry operations, including translations, reflections, and rotations. These groups help in understanding how patterns can be arranged and repeated, making them important in fields like crystallography, textile design, and architecture. By studying frieze groups, one can predict how a design will look when extended infinitely in one direction.