  It is proved that for a system of spins $\sigma _i = \pm 1$ having an
interaction energy $-\sum K_{ij} \sigma _i \sigma _j $ with all the $K_{ij}$
strictly positive,one can construct a dual formulation by associating a dual
spin $S_{ijk} = \pm 1$ to each triplet of distinct sites $i,j$ and $k$. The
dual interaction energy reads $-\sum _{(ij)} D_{ij} \prod _{k \neq i,j}
S_{ijk}$ with $tanh(K_{ij})\ = \ exp(-2D_{ij})$, and it is invariant under
local symmetries. We discuss the gauge-fixing procedure, identities relating
averages of order and disorder variables and representations of various
quantities as integrals over Grassmann variables. The relevance of these
results for Polyakov's approach of the 3D Ising model is briefly discussed.
