Hyperbolic Tessellation — Poincaré Disk

{p,q} tilings in the hyperbolic plane — infinite regular tessellations

The Poincaré disk model of H² maps the entire hyperbolic plane into a unit disk. Geodesics are circular arcs perpendicular to the boundary. In {p,q} tessellation, p-gons meet q at each vertex. Any {p,q} with (p−2)(q−2) > 4 tiles the hyperbolic plane — infinitely many tilings, all distinct from Euclidean geometry. Drag the disk to apply a Möbius transformation and explore different centers.