Hyperbolic Tiling — Poincaré Disk

In the Poincaré disk model of hyperbolic geometry, geodesics appear as circular arcs perpendicular to the boundary. This {p,q} tiling uses p-gons with q meeting at each vertex. All tiles are congruent in hyperbolic space — the apparent shrinking near the boundary is a property of the embedding, not the geometry.

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Drag to rotate. Tilings exist for all p,q where 1/p + 1/q < 1/2 (hyperbolic), = 1/2 (Euclidean), > 1/2 (spherical).