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

2015/08/08 by Sugimoto, Teruhisa
#05B45 #52C20 #52C23 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1508.01864

Abstract

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

Related

• Exhaustive search of convex pentagons which tile the plane
• Aperiodic sets of three types of convex polygons
• Properties of Convex Pentagonal Tiles for Periodic Tiling
• Old problem revisited: Which equilateral convex polygons tile the plane?
• Convex pentagons and convex hexagons that can form rotationally symmetric tilings