I probably should have pointed out in my last post that the solution to the
problem of the effective resistance across two nodes of a regular nearest-
neighbor-bond-connected Bravais lattice is essentially the so-called
'lattice Green's function' (times bond resistance r) corresponding to the
lattice of interest. Such a Green's function has other applications in
problems in math & solid state physics (e.g. finding escape/return
probabilities for a random walker on a lattice among other things).