Conformal Tiling on a Torus

John M. Sullivan
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 593–596 Short Papers


Given a regular tiling of the torus, we want to depict it on a torus in space with as much conformal symmetry as possible. In particular, the conformal type of the surface should agree with that implied by the regular tiling, and symmetries not seen as Euclidean motions should be represented, whenever possible, by Möbius transformations.