  In a recent paper, we have reported a universal power law for both site and
bond percolation thresholds in any Bravais lattice with q equivalent nearest
neighbors in dimension d. We now extend it to three different classes of
lattices which are, respectively, anisotropic lattices whith not equivalent
nearest neighbors, non-Bravais lattices with two atom unit cells, and
quasicrystals. The investigation is focussed on d=2 and d=3, due to the lack of
experimental data at higher dimensions. The extension to these lattices
requires the substitution of q by an effective (non integer) value $q_{eff}$ in
the universal law. For each out of 17 lattices which constitute our sample, we
argue the existence of one $q_{eff}$ which reproduces both the site and the
percolation threshold, with a deviation with respect to numerical estimates
which does not exceed $\mp 0.01$.
