From fingertip grasp to power grasp, a multifingered robot hand takes various configurations. Most of the previous statics theories about grasping and manipulation were established under the assumption that the contact points are on the fingertips. In this article, under the generalized contact assumption that allows multiple contacts and face contacts anywhere on hand surface, we establish the statics theory for grasping and manipulation that is applicable to all the grasping configuration, using the theory of polyhedral convex set. The relation between the external force acting on the object and joint torques is made clear, and the foundation of the statics theory is formed. The algorithms for computing admissible external force space and critical external force space are proposed. Finally, the validity of our approach is illustrated by a numerical example and experiments