Are the convex mono-tiles that only admit periodic edge-to-edge tilings classified? If so, can you give a reference?
I tried to find answers to this question and related information on the web, but was not successful. I am aware that for some tiles (such as rectangles) it is easy to construct non-periodic tilings, but could not find any information concerning the opposite. It could be that the question is too simple to be interesting or at the other extreme unsolved (the latter seems very unlikely, as my searches have come up empty).