There exists an entropy-preserving equivariant surjective map from the d-dimensional critical sandpile model to a certain closed, shift-invariant subgroup of the Cartesian product of infinitely many cycles, one for each node of the d-dimensional integer lattice (the 'harmonic model'). A similar map can be constructed for the dissipative abelian sandpile model and be used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model. (Joint work with Evgeny Verbitskiy)