HYPERBOLIC TILINGS — POINCARÉ DISK

TILING {p,q}

Polygon sides p 5 Vertex valence q 4

PRESETS

DISPLAY

Recursion depth 5 Color by depth
Show disk boundary

In the Poincaré disk model of the hyperbolic plane, geodesics are circular arcs orthogonal to the boundary. The {p,q} tiling has p-gons meeting q at each vertex. When (p-2)(q-2)>4 the tiling is hyperbolic. Infinitely many tiles fit in finite area — the boundary circle is infinitely far away.