This applet draw a set of set of wallpaper pattern, which are repeating patterns which fill the plane and exhibit certain mathematics symmetries. There are only 17 different possible types which fill the plane and the different patterns have been known for quite a long time now.
All types have two translation symmetries which define a lattice.
CM A reflection and a glide reflection along parallel axes. Also has a 180 degree rotation. The translation directions are at right angles and there is a reflection along one of these. Also has two 180 deg rotations. Also has a 180 deg rotation.