Percolation thresholds of the duals of the face-centered-cubic, hexagonal-close-packed, and diamond lattices

A calculation of percolation thresholds of the dual lattices of the face-centered-cubic (fee) lattice, the hexagonal-close-packed (hcp) lattice, and the diamond lattice is presented. The results are used to investigate whether these thresholds can be related to the thresholds of the fcc, hcp, and diamond lattices themselves. In two dimensions there is such a relation, but the present results indicate that there is no such relation in three dimensions. Also, the site percolation threshold of the dual of the diamond lattice turns out to be high: Although the average coordination number q of this lattice is 6 2/3, its site percolation threshold is higher than for many lattices with q=5.