  The star-triangle transformation is used to obtain an equivalence extending
over the set of all (in)homogeneous bond percolation models on the square,
triangular and hexagonal lattices. Among the consequences are box-crossing
(RSW) inequalities for such models with parameter-values at which the
transformation is valid. This is a step toward proving the universality and
conformality of these processes. It implies criticality of such values, thereby
providing a new proof of the critical point of inhomogeneous systems. The
proofs extend to certain isoradial models to which previous methods do not
apply.
