On the number of non-hexagons in a planar tiling

TL;DR

This paper provides a straightforward proof that in any normal tiling of the plane with convex polygons having at least six sides, only finitely many tiles are not hexagons, with the rest being hexagons.

Contribution

The paper offers a simple proof of Stehling's result regarding the prevalence of hexagons in such tilings, simplifying previous approaches.

Findings

Almost all tiles are hexagons in the tiling.

Finite number of non-hexagonal tiles exist.

Proof simplifies understanding of convex polygon tilings.

Abstract

We give a simple proof of T. Stehling's result, that in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except the finite number are hexagons.