3 Tessellating Regular Polygons

After reading the interesting blog on the new "pi", you threw in the question of why are there only three regular polygons. Well, I was quite intrigued by this as I figured that there would surely be at least one more but thinking a little bit more on it, I figured something like a pentagon wouldn't be able to completely surround itself with more regular pentagons as there would be extra space between the repeating shapes. My theory was confirmed when I went to this site which put my brief and simple explanation into a genuine one with actual reasoning. It stated that the following regular polygons each had interior angles which divided evenly into 360 degrees; the triangle at 60 degrees, the square at 90 and the hexagon at 120. Due to this, the uniform tessellation (uniform meaning all polygons at one vertex are of the same type) is possible without any extra "space" as I had thought of at the start.