There are three classes of isohedral convex hexagon tilings. The regular hexagon is in all three. [br][br]This is number two![br][br]It has two pairs of congruent sides, and three angles that always add to 360 degrees. The tiling has two midpoint 180 degree rotations and a sweet glide reflection.

One annoying bit: two of the edge alterations collapse when you change the bunderlying hexagon. Can't figure out how to fix it. It's a side effect of making them dependent on the main vertices.