Frieze pattern are widely used in architecture and art. These are two dimensional repetitive patterns in one direction. As they all have translational symmetry. A little bit of combinatorial argument along with composition of symmetries can easily reveal why we have only 7 frieze patterns.
![Why 7 frieze pattern](https://sumantmath.wordpress.com/wp-content/uploads/2020/08/the-seven-frieze-patterns-1.png?w=1024)