Convex Pentagons with Positive Heesch Number

TL;DR

This paper classifies convex pentagons with a Heesch number of one that can form edge-to-edge coronas, expanding understanding of tiling properties of convex polygons.

Contribution

It introduces a new classification scheme for convex pentagons with Heesch number one capable of edge-to-edge coronas, a novel insight in polygon tiling theory.

Findings

Identified convex pentagons with Heesch number one

Established conditions for edge-to-edge coronas in these pentagons

Provided a comprehensive classification of these polygons

Abstract

We found convex pentagons whose Heesch number is equal to one, and which admit an edge-to-edge corona. In this manuscript, we present a new classification of these convex pentagons.