Exhaustive search of convex pentagons which tile the plane
classification
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convexexhaustivefamiliespentagonsplanesearchtheretile
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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.
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Forward citations
Cited by 2 Pith papers
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Unboundedness of the Heesch Number for Hyperbolic Convex Monotiles
Resolves the Heesch problem by showing unbounded Heesch numbers for homogeneous tilings and convex monotiles in the hyperbolic plane, with first examples of weakly aperiodic convex monotiles from dual homogeneous tilings.
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Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons
Investigates edge-to-edge spherical tilings by angle-congruent pentagons and the impact of reducing angle distinctions.
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