English

Hexagonal Tiling of the Plane

Combinatorics 2026-04-29 v2 History and Overview Metric Geometry

Abstract

Since the thesis of K. Reinhardt in 1918, it is well known that there are exactly three types of convex hexagons that can tile the plane. However, the proof of the fact is far from being complete. We prove this fact, under an assumption weaker than the convexity.

Keywords

Cite

@article{arxiv.2508.01404,
  title  = {Hexagonal Tiling of the Plane},
  author = {Ze Zhu and Erxiao Wang and Min Yan},
  journal= {arXiv preprint arXiv:2508.01404},
  year   = {2026}
}

Comments

39 pages, 24 figures

R2 v1 2026-07-01T04:31:07.505Z