Bridges 2010 Regular Paper

My Search for Symmetrical Embeddings of Regular Maps
Carlo H. Séquin
(Proceedings pages 85–94)


Various approaches are discussed for obtaining highly symmetrical and aesthetically pleasing space models of regular maps embedded in surfaces of genus 2 to 5. For many cases, geometrical intuition and preliminary visualization models made from paper strips or plastic pipes are quite competitive with exhaustive computer searches. A couple of particularly challenging problems are presented as detailed case studies. The symmetrical patterns discovered could be further modified to create Escher-like tilings on low-genus handle bodies.