English

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

R2 v1 2026-06-22T12:54:12.996Z