Why do only the triangle hexagon and square tile?

It's not because of a natural law or something; it's inherent in the structure of space, and the shapes of triangles, hexagons, and squares. Your question is like asking, "why does 2 + 2 = 4?" There's not a reason, they just do because that's how things are.

Also, they aren't the only shapes that tile, just the only regular polygons that tile.

>>M.T.<<

Think it has to do with the fact that for a shape to tile the measure of the interior angle multiplied times something has to give you 360, if not the shape cannot tile