Options for grasping an object are restricted by the surface on which the object is placed. There is a frequent need therefore, to manipulate the object from an initial lifting grasp to a final working one. We present here an algorithm for finding the three-finger force-closured grasp space of polygonal objects for arbitrarily small friction (certain particular solutions for smooth objects are also given). Using a graphical representation of the grasp space we determine conditions for manipulating an object from one grasp to another with four fingers and arbitrarily small friction. Planning possibilities for the manipulation process are also presented.