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