Conformally correct tilings
Saul Schleimer, Henry Segerman
TL;DR
This paper explores methods for creating conformally accurate tilings of compact surfaces, demonstrating an example with a hyperbolic (2, 4, 6) triangle tiling on the Chmutov surface.
Contribution
It introduces techniques for producing conformally correct Euclidean and hyperbolic tilings, including a specific example on the Chmutov surface.
Findings
Successful tiling of the Chmutov surface with hyperbolic triangles
Methods for achieving conformal accuracy in surface tilings
Illustration of art and science in geometric tiling
Abstract
We discuss the art and science of producing conformally correct euclidean and hyperbolic tilings of compact surfaces. As an example, we present a tiling of the Chmutov surface by hyperbolic (2, 4, 6) triangles.
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Taxonomy
TopicsArchitecture and Art History Studies · Architecture and Computational Design · 3D Shape Modeling and Analysis