Hyperbolic Tilings — H²

Poincaré disk model — {p,q} tessellations where (p-2)(q-2) > 4.

Tiling {p, q}

In the hyperbolic plane, a {p,q} tiling has p-gons meeting q at each vertex.

Condition: (p−2)(q−2) > 4 for hyperbolic geometry. Euclidean is = 4, spherical is < 4.

Color encodes depth (generation) from the central tile. The disk boundary is the "circle at infinity" — points at infinite hyperbolic distance.

All tiles are congruent in hyperbolic geometry despite appearing smaller near the boundary.