  The aim of this paper is to explore possible ways of extending Smirnov's
proof of Cardy's formula for critical site-percolation on the triangular
lattice to other cases (such as bond-percolation on the square lattice); the
main question we address is that of the choice of the lattice embedding into
the plane which gives rise to conformal invariance in the scaling limit. Even
though we were not able to produce a complete proof, we believe that the ideas
presented here go in the right direction.
