There are 17 types of symmetry which can used to cover a 2 dimensional surface.

Here are some websites that discuss this.

Detailed discussion of computer generated Zelij patterns:

http://www.mi.sanu.ac.yu/vismath/kaplan/index.html

The basic table of symmetries:

http://www2.spsu.edu/math/tile/symm/ident17.htm

From the same website – an example of a pattern from the Al Hambra with p6m symmetry:

http://www2.spsu.edu/math/tile/grammar/moor/moor3f.htm

The Wikipedia page on rotational symmetry

http://en.wikipedia.org/wiki/Symmetry_combinations

82 Zelij pics on Flickr. I must add mine…

http://www.flickr.com/photos/tags/zelij/interesting/

Dutch artist MC Escher was a master of tiling symmetries

Douglas Hofstadter, ‘Visions of Symmetry’

Tile Generator (design your own replicating tile structure):

http://escher.epfl.ch/escher/

Dr Heinrich Heesch identified 28 types of repeating structure

http://www.eschertile.com/tile28.htm