http://www.shodor.org/interactivate/activities/Tessellate/
http://gwydir.demon.co.uk/jo/tess/tess.htm
http://gwydir.demon.co.uk/jo/tess/tri.htm
Now, what happens if you "force" shapes to tessellate by joining your gaps? Look at these hexagons and pentagons:
By forcing the shapes to not have gaps, the structure takes on a curved shape, resulting in a truncated icosahedron (a.k.a. soccer ball).
This website, named for Archimedes, is fantastic for acquainting yourself with polyhedra. (Notice "poly"? Think word study.)
