  The site percolation thresholds p_c are determined to high precision for
eight Archimedean lattices, by the hull-walk gradient-percolation simulation
technique, with the results p_c = 0.697043, honeycomb or (6^3), 0.807904
(3,12^{2}), 0.747806 (4,6,12), 0.729724 (4,8^{2}), 0.579498 (3^{4},6), 0.621819
(3,4,6,4), 0.550213 (3^{3},4^{2}), and 0.550806 (3^{2},4,3,4), and errors of
about +/- 2\times10^{-6}. (The remaining Archimedean lattices are the square
(4^4), triangular (3^6) and Kagom\'e (3,6,3,6), for which p_c is already known
exactly or to a high degree of accuracy.) The numerical result for the
(3,12^{2}) lattice is consistent with the exact value [1-2 sin(\pi/18)]^{1/2},
which we also derive.
  The values of p_c for all Archimedean lattices are found to be linearly
related to the density of sites within an error of about 1%, which predicts p_c
more accurately than correlations based just upon the coordination number can
give. Comparison with anisotropic lattices is also made.
