In the wollowing applets
you can see so called ornament or wallpaper groups.
The transformations involved are
translation, reflection, glide reflection, and rotation.
There are only 17 non-isomorphic 17 ways to
combine them to form a wallpaper group.
You should also have a look at the Morenament programm by Martin von Gargern, where you can freely play with these groups.
