Heesch's Tiling Problem
Casey Mann · American Mathematical Monthly · 2004
1. INTRODUCTION. Let T be a tile in the plane. By calling T a tile, we mean that T is a topological disk whose boundary is a simple closed curve. But also implicit in the word “tile ” is our intent to use congruent or reflected copies of T to cover the plane without gaps or overlapping; that is, we want to tessellate the plane with copies of T. In a minor abuse of language, one often speaks of T (as opposed to copies of