Transformations and SymmetryCrystallographic Groups

The wallpaper groups were all about flat, two-dimensional patterns. We can do something similar for three-dimensional patterns: these are called crystallographic groups, and there are 219 of them!

In addition to translations, reflections, rotations, and glide reflections, these groups include symmetries like glide planes and screw axes (think about the motion when unscrewing a bottle).