The Poincaré disk compresses the entire hyperbolic plane into a unit disk. In this model,
geodesics are circular arcs perpendicular to the boundary. A {p,q} tiling places regular p-gons
with q meeting at every vertex — impossible in Euclidean geometry when (p−2)(q−2) > 4.
All polygons are geometrically equal in hyperbolic space despite looking smaller near the edge.