wallpaper groups

Wallpaper groups are a way mathematicians classify repeating patterns, like those on wallpaper or tiles, based on their symmetry. They describe how a pattern can be shifted, rotated, or reflected to look the same, capturing all the ways a pattern repeats in two dimensions. There are 17 such groups, each representing a unique combination of symmetries. This classification helps us understand the underlying structure of decorative designs and naturally occurring patterns, revealing the mathematical rules governing visual repetition and symmetry in the world around us.