Tiling the Plane

An example of tiling the plane with regular hexagons.  Well, maybe not the whole plane, but you get the idea.

A valid tiling of the plane means that everything fits together perfectly–no gaps.

A nice simple little exercise is trying to figure out which regular polygons can be used to tile the plane like this.  The next step is to allow the use of more than one kind of regular pentagon, and so on.