Binary tiling: Difference between revisions

Revision as of 18:52, 27 October 2024

Revision as of 18:52, 27 October 2024

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[[File:Hyperbolic binary tiling.png|alt=Binary tiling on Poincare disk|thumb|A binary tiling in the [[Poincaré disk model]] of the [[hyperbolic plane]]. Each tile edge lies on a [[horocycle]] (shown as circles interior to the disk) or a hyperbolic line (arcs perpendicular to the disk boundary). The horocycles and lines are asymptotic to an [[ideal point]] located at the right side of the Poincaré disk.]]

In [[geometry]], a '''binary tiling''' (sometimes called a '''Böröczky tiling'''){{r|df}} is a [[tiling of the hyperbolic plane]], resembling a [[quadtree]] over the [[Poincaré half-plane model]] of the hyperbolic plane. The tiles are congruent, each adjoining five others. They may be convex [[pentagon]]s, or non-convex shapes with four sides, alternatingly line segments and [[horocycle|horocyclic]] arcs, meeting at four right angles.