168 Butterflies on a Polyhedron of Genus 3

Douglas Dunham
Bridges: Mathematical Connections in Art, Music, and Science (2002)
Pages 197–204


In 1985 the mathematician H. S. M. Coxeter suggested that one could cover a torus in a regular way with 18 copies of the butterfly motif of M. C. Escher's Notebook Drawing Number 70. In this paper, we show how 168 copies of that motif can cover a surface of genus 3 - a 3-holed torus. In fact, we cover a polyhedron of genus 3 with such butterflies.