Tilings 1 to 19. The arrow is from vertex s1 to s2 in the bold tile. © Michaël Rao

Abstract
We present an exhaustive search of all families of convex pentagons which tile the plane. This research shows that there are no more than the already 15 known families. In particular, this implies that there is no convex polygon which allows only non-periodic tilings.
References : Exhaustive search of convex pentagons which tile the plane. Michaël Rao, Arxiv.org, arXiv:1708.00274