Hyperbolic Poincaré Disk Tiling

The entire hyperbolic plane packed into the unit disk — {p,q} tessellations where (p−2)(q−2) > 4

Polygon sides p 5

Valence q 4

Depth 3

Rotation 0°

Poincaré disk: geodesics are circular arcs meeting boundary at 90°. Angle sum of triangle = π − Area/K (K=−1).
Valid tilings require (p−2)(q−2) > 4. Shown: {p,q} = {5,4}