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Planning of a dextrous manipulation task for a multifingered hand requires the feasibility of all the grasps involved throughout the manipulation process. In this paper, we address the problem of determining whether a desired grasp of a polyhedral object is kinematically feasible. In our study, we define a grasp in terms of a system of contact pairs between the topological features of the hand and the object, and formulate the grasp feasibility analysis as a set of equality and inequality constraints in the variables of the hand and object configurations. The feasibility of a grasp then becomes equivalent to the simultaneous satisfaction of all the constraints. This allows us to cast the feasibility analysis conveniently as a constrained nonlinear optimization problem and solve it numerically with commercially available software. The effectiveness of our approach is illustrated with an example of grasping a cuboid using a three-fingered robotic hand.