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The atomistic structure of the graphene buffer layer on Si-terminated SiC is investigated using a modified version of the environment-dependent interatomic potential. The determination of the equilibrium state by the conjuguate gradients method suffers from a complex multiple-minima energy surface. The initial configuration is therefore modified to set the system in specific valleys of the energy surface. The solution of minimal energy forms a hexagonal pattern composed of stuck regions separated by unbonded rods that release the misfit with the SiC surface. The structure presents the experimental symmetries and a global agreement with an ab initio calculation. It is therefore expected that the interatomic potential could be used in classical molecular dynamics calculations to study the graphene growth.