Thinking over the question of why there are only three
regular polygons that tessellate I began visualizing a picture in my head. The reason the hexagon, triangle, and square are the only regular polygons to tessellate is because of their angles. 360 is divisible by the angles of all three of these polygons. The polygons all tessellate at one point which means for them to tessellate the polygons need to be able to go around the certain point enough times that there are no spaces in between them. A regular triangle has angles of 60 degrees, therefore it will go around a certain point six times and repeat at different points. A square with angles of 90 degrees will only go around 4 times and a hexagon with angles of 120 degrees will only go around 3 times. All equaling 360.
