Similarity of percolation thresholds on the HCP and FCC lattices

Extensive Monte Carlo simulations were performed in order to determine the precise values of the critical thresholds for site (p(e,S)(hep) = 0.199 +/- 0.000 001 0) and bond (p(c,B)(hcp) = 0.120 1640 +/- 0.000 001 0) percolati on on the hcp lattice to compare with previous precise measurements on the fee lattice. Also, exact enumeration of the hcp and fee lattices was perfor med and yielded generating functions and series for the zeroth, first, and second moments of both lattices. When these series and the values of p(c) a re compared to those for the fee lattice, it is apparent that the site perc olation thresholds are different; however, the bond percolation thresholds are equal within error bars, and the series only differ slightly in the hig her order terms, suggesting the actual values are very close to each other, if not identical.