Convex Polygons for Aperiodic Tiling
Metric Geometry
2017-12-27 v2
Abstract
If all tiles in a tiling are congruent, the tiling is called monohedral. Tiling by convex polygons is called edge-to-edge if any two convex polygons are either disjoint or share one vertex or one entire edge in common. In this paper, we prove that a convex polygon that can generate an edge-to-edge monohedral tiling must be able to generate a periodic tiling.
Keywords
Cite
@article{arxiv.1602.06372,
title = {Convex Polygons for Aperiodic Tiling},
author = {Teruhisa Sugimoto},
journal= {arXiv preprint arXiv:1602.06372},
year = {2017}
}
Comments
8 pages, 7 figures