Wallpaper Group

Wallpaper groups are a way to classify repeating patterns based on their symmetrical properties. Imagine a pattern that can be shifted, rotated, reflected, or flipped and still look the same—a wallpaper group describes all such symmetry operations combined into 17 distinct categories. These groups help mathematicians and artists understand the underlying structure of complex, repeating designs found in fabric, tiles, and nature. Essentially, wallpaper groups organize how patterns repeat and transform, revealing the mathematical beauty behind visually appealing, seamless designs.