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This note concentrates on removing redundancy in the set of constraints for the multiparametric quadratic problems (mpQP) related with the constrained predictive control. The feasible domain is treated as a parameterized polyhedron with a focus on its parameterized vertices. The goal is to find a splitting of the parameters (state) space corresponding to domains with regular shape (nonredundant constraints), resulting in a table of regions where the constraints have a minimal representation, so that the online optimization routines can act with better performances. The procedure can be seen as a preprocessor either for the classical QP methods or for the routines based on explicit solutions. For important degrees of redundancy, the proposed technique may bring computational gains for real-time application or on the complexity of the positioning mechanism for evaluating the explicit solution.