Hexagonal Tiling of the Plane

TL;DR

This paper revisits the classification of convex hexagons that can tile the plane, providing a more complete proof under weaker assumptions than convexity.

Contribution

It offers a new proof of the classification of hexagonal tilings, extending the known results to a broader class of shapes with weaker assumptions.

Findings

Confirmed only three types of convex hexagons tile the plane.

Provided a more complete proof under weaker assumptions than convexity.

Extended the understanding of hexagonal tilings beyond convex shapes.

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.