The remaining patterns number 2449 are all *wallpaper patterns* and repeat in one of 17 ways. The most important characteristic is that of *rotations*.
Hence we divide these patterns according to the maximal rotation present.

The first group are examples of patterns with no rotations. An example of two of these are:

The second group are examples of patterns with rotations of order 2. An example of two of these are:

The third group are examples of patterns with rotations of order 3. An example of two of these are:

The fourth group are examples of patterns with rotations of order 4. An example of two of these are:

The fifth group are examples of patterns with rotations of order 6. An example of two of these are:

v45