To answer the question of how many shapes tesselate and why?: There are only three shapes that tessellate. The reason there are only three shapes that tesselate has to do with the interior angles and their measures. There are only three shapes that when placed together so that the vertices of the shapes meet to form one point, the angles that this forms have to equal 360 degrees. If the interior angles do not sum to this then there will not be a whole number of shapes surrounding that center point, leaving you with pieces of shapes. There are only 3 shapes that will form interior angles that form 360 degrees, and that will tessellate.