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Tiling With Pentagons

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A pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. The plane cannot be tiled with regular pentagons. However, are there any convex pentagons that can tile the plane? This session explores various pentagons and their tiling abilities. From 1918 to 1985, fourteen irregular pentagons that would tile the plane were discovered. On August 14, 2015, Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell announced that they discovered a fifteenth pentagon. Interestingly, in 2017, Michaël Rao proved that there were no more than these...