The Seventeen Wallpaper Groups

The ornamental groups of the plane are the rosette groups, the frieze groups, and the wallpaper groups. The rosette groups are the finite groups of isometries, which by Leonardo’s Theorem are the groups C_n and D_n. A frieze group is a group of isometries whose subgroup of translations is generated by one translation. Frieze groups were treated in Chapter 10. We now turn to the last of the ornamental groups of the plane by considering groups whose subgroup of translations is generated by two translations.