Decorating Regular Tiles with Arcs

David A. Reimann
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 581–584 Short Papers


This paper introduces a notation for describing a regular polygon tile decorated with arcs. Given a tile decorated with a number of arcs having endpoints uniformly spaced around the polygon, the number of possible decorated tiles is given, including the special case where no arcs intersect. The tiles decorated in this manner provide an enormous number of patterns.