Mertens, S.,Moore, C.

We use invasion percolation to compute numerical values for bond and site percolation thresholds pc (existence of an infinite cluster) and pu (uniqueness of the infinite cluster) of tesselations {P, Q} of the hyperbolic plane, where Q faces meet at each vertex and each face is a P-gon. Our values are accurate to six or seven decimal places, allowing us to explore their functional dependency on P and Q and to numerically compute critical exponents. We also prove rigorous upper and lower bounds for pc and pu that can be used to find the scaling of both thresholds as a function of P and Q.