Percolation thresholds on a triangular lattice for neighborhoods containing sites up to the fifth coordination zone

We determine thresholds $p_c$ for random-site percolation on a triangular lattice all available neighborhoods containing sites from the first to fifth coordination zones, including their complex combinations. There are 31 distinct neighbourhoods. The dependence of value number $z$ tested against various theoretical predictions. newly proposed single scalar index $\xi=\sum_i z_ir_i^2/i$ (depending zone $i$, neighbourhood and square-distance $r^2$ in $i$-th central site) allows differentiate among neighbourhoods relate $\xi$. roughly follow power law $p_c\propto\xi^{-\gamma}$ with $\gamma\approx 0.710(19)$.