The planning problem associated with tactile exploration for object recognition and localization is addressed. Given that an object has been sensed and is one of a number of modeled objects, and given that the data obtained so far are insufficient for recognition and/or localization, the methods developed determin the paths along which a point contact sensor must be directed in order to obtain further highly diagnostic measurements. Three families of sensor paths are found. The first is the family of paths for which recognition and localization are guaranteed. The second guarantees only that something will be learned. The third represents paths to avoid because nothing new will be learned. The methods are based on a small but powerful set of geometric ideas and are developed for two-dimensional, planar-faced objects. They are conceptually easily generalized to handle three-dimensional objects, including objects with through holes.>