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This paper discusses how data from multiple tactile sensors may be used to identify and locate one object, from among a set of known objects. We use only local information from sensors: 1) the position of contact points and 2) ranges of surface normals at the contact points. The recognition and localization process is structured as the development and pruning of a tree of consistent hypotheses about pairings between contact points and object surfaces. In this paper, we deal with polyhedral objects constrained to lie on a known plane, i.e., having three degrees of positioning freedom relative to the sensors. We illustrate the performance of the algorithm by simulation.