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We show that convex pentagons that can generate edge-to-edge monohedraltilings of the plane can be classified into exactly eight types. Using theseresults, it is also proved that no single convex polygon can be an aperiodicprototile without matching conditions other than "edge-to-edge."

Tiling Problem: Convex Pentagons for Edge-to-Edge Monohedral Tiling and Convex Polygons for Aperiodic Tiling