Draw a repeating pattern and the site names its plane group, with the mirrors, glides and rotation centres marked on the tiling it generates.
The seventeen wallpaper groups cover every way a motif can repeat in two directions; the seven frieze groups cover repetition along one.
Molecular point groups with their operations and character tables, the 230 space groups with a cell builder, and the 17 wallpaper and 7 frieze groups drawn live. The tool needs JavaScript, and WebGL2 for the 3D views; these are the pages it offers: