There are only three regular polygons that tessellate on the Euclidean
plane. These polygons include triangles, squares and hexagons. I recently found out what it even meant for something to "tessellate". I did an artistic project involving the, a while ago, but I have long forgotten the actual definition. One with no knowledge on this matter, in other words, me prior to some research, would think that "to tessellate" is to decorate a surface with mosaics, but in the math world, a tessellation is what's created when a single shape, is copied and repeated throughout a whole plane, covering every area and leaving no gaps. Regular tessellations are made up of congruent regular polygons. It makes sense for a hexagon to be capable of regular tessellation considering 6 triangles make up a hexagon, but the reason that triangles, squares, and hexagons are the only regular polygons that tessellate, is because the interior angles of these three shapes, (60, 90, and 120 degrees), are exact divisors of 360. It is possible to create tessellations using a variety of different polygons in a repeated and uniform pattern, but that is not considered a regular tessellation. Tessellations are not only mind boggling to grasp the concept of, but when you put color and flare onto them, they are truly beautiful. Having mathematical knowledge about them is not only useful in the world of numbers and shapes, but in architecture and decorating as well.http://mathforum.org/sum95/suzanne/whattess.html
