Gábor's Tiling
Math Munch featured this tiling, from a tile competition called Scientile.
Gábor designed it to fit together in several ways, so the tilings are especially nice. The fundamental region is like two blue rhombi from the patternblocks. To be exactly his design, you have only one side free. If you give up one of the translational symmetries, you can have two.
Math Munch post: http://mathmunch.org/2016/01/06/2016-scientile-and-a-new-algorithm/
Scientile submissions: http://spidron.hu/scientile/submissions.html