Conformally correct tilings

2016/12/25 by Schleimer, Saul, Segerman, Henry
#49Q10 #51F15 #53A05 #65D17 #FOS: Mathematics #Geometric Topology (math.GT) #History and Overview (math.HO)

paper · doi:10.48550/arxiv.1612.08299

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.

Related

• Conformal Tilings, Combinatorial Curvature, and the Type Problem
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• Characterization of the Two-Dimensional Five-Fold Translative Tiles
• Decorated discrete conformal maps and convex polyhedral cusps
• Multiple Translative Tilings in Euclidean Spaces