Inspired by a beautiful hexagon tiling by Regolo54,
[url]http://regolo54.tumblr.com/post/131277473282/geometry[/url]
It was very interesting to try to generalize.
This uses two layers of rotational symmetry to make tessellations. Rather than restrict it to where it works out perfectly, I liked some of the effects possible from the non-3,4,5,6,8,12 cases.
The double checkbox is because the amount of the angle needed for the 2nd rotation varies and I took the easy way out.