The first wallpaper symmetry is the simplest. It is comprised of two translations
only.
Consider the infinite tiling of the plane by parallelograms.
Supposes you have two copies of the tiling; one lying on top of the
other. Pick up the top tiling and select any translation parallel
to an edge of the parallelogram. Use this translation to shift the
whole tiling one tile's width. Now set
the tiling back down. The displaced tiling matches the bottom
tiling perfectly! This is what we mean when we say a tiling
possesses the symmetry p1.
Mathematicians say such a tiling is symmetric with respect to
translation. This is such a basic and important kind of
symmetry, it has a special name. These tiling are periodic.
Kali denotes this symmetry by "0". You can go to now to experiment with symmetry p1.
