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
Exhaustive search of convex pentagons which tile the plane (publication on Arxiv.org)
Michaël Rao
LIP (Computer Science Laboratory)
Pentagon Tiling Proof Solves Century-Old Math Problem (article in Quanta Magazine)
Exhaustive search of convex pentagons which tile the plane
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