The Symmetry of “Circle Limit IV” and Related Patterns

Douglas Dunham
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 163–168 Regular Papers


M.C. Escher's print Circle Limit IV is the last of his four “Circle Limit” patterns. There are two questions that can be asked about the symmetry of Circle Limit IV. First, what is the correct orientation in which to display the print? Second, what is the symmetry group of the pattern? We answer those questions and show some new patterns related to Circle Limit IV.