Poincaré disk model: infinite hyperbolic plane inside a circle
The Poincaré disk model represents the entire hyperbolic plane within a unit disk. Straight lines ("geodesics") are arcs of circles perpendicular to the boundary. A {p,q} tiling places p-gons with q meeting at each vertex. Unlike Euclidean tilings, infinitely many regular tilings exist since the angle sum of hyperbolic polygons can be made arbitrarily small.