The Swiss mathematician Ludwig Schläfi showed that there are eight semiregular tessellations of a plane. See also the Islamic Tilings for a dazzling exploration of semiregular and related tilings, beautifully worked in ceramics.
The English mathematician Roger Penrose has devised some Aperiodic Tilings using a small set of regular tiles. These fill the plane but never repeat!
Incidentally, the name tessellation derives from the Greek
Tessera, meaning 4, square, tile. Obviously, 4-square tiles are the easiest to make and fit together (and the way that your web browser tiles your screen!).
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All images and text (c) Ian Alexander 1996-2005
Please obtain my written permission for commercial use