We define a fundamental domain of a linear programming relaxation of a combinatorial integer program which is symmetric under a group action. We then provide a construction for the polytope of a fundamental domain defined by the maximization of a linear function. The computation of this fundamental domain is at worst polynomial in the size of the group. However, for the special case of the symmetric group, whose size is exponential in the size of the integer program, we show how to compute a separating hyperplane in polynomial time in the size of the integer program.
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