A word after a word after a word is power. Add citations directly into your paper, Check for unintentional plagiarism and check for writing mistakes. Need to save your citations for later? Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the simpler frieze groups and the three-dimensional space groups. Wallpaper groups categorize patterns by their symmetries. A symmetry of a pattern is, loosely speaking, a way of transforming the pattern so that it looks exactly the same after the transformation.