Wallpaper Groups

We have been examining frieze groups, which are symmetries in one dimension. The repeated part of our design is allowed to go only in a straight line.

The Kali program also lets you draw using wallpaper groups, which are symmetries in the plane. Patterns with symmetries in the plane are called wallpaper patterns. In wallpaper patterns, a design may be repeated in more than one direction. Here some examples:



Since wallpaper patterns use one more dimension than frieze patterns, there are more combinations of symmetries that a wallpaper pattern may have. While there are only 7 frieze groups, there are 17 wallpaper groups.