Symmetry 2
There are 4 ways of moving a motif to another position in the pattern. These were described by Escher, and Doris Schattschneider has drawn a diagram, using his creatures, to explain it.
Symmetry is a complex mathematical subject and, as stated earlier, this site is here to encourage the graphical aspect. There are several excellent sites on the Internet which cover the maths side and give graphical examples (see links in site info) and I also recommend 2 books - click next button.