Escherized Hexagon 2
There are three classes of isohedral convex hexagon tilings. The regular hexagon is in all three.
This is number two!
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.