Conformal Tiling on a Torus

Year: 2011 Authors: John M. Sullivan

Core claim

Regular torus tilings and periodic patterns can be embedded in space so their conformal type and as many symmetries as possible are visible, often as Möbius transformations.

Topics

conformal geometry, torus embeddings, regular tilings, symmetry, Hopf fibrations

Domains

complex analysis, surface geometry, tiling theory, topology, group symmetry, mathematical visualization, architectural form, pattern design

Methods

conformal embedding, stereographic projection, Hopf fibration, energy minimization, Surface Evolver

Media

round torus, flat torus, sphere S^3, diagrams, grid lines

Source status

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