Effective object acquisition and/or manipulation requires that the agent can deal with geometrical relations of the objects with respect to the body. In haptics such relations are established via contact of the object with the skin and kinesthesis during manipulation. An a priori framework is perhaps available via prior experience which is possibly based on multiple modalities. When haptics is the only modality permitted in the execution of the actual task this framework may be denoted "haptic space". Whereas numerous experiments have elucidated the structure of optical space, haptic space remains - despite its obvious importance - largely virgin territory. We propose a fairly extensive exploration of haptic space in so far as it involves movements of arms, hands and fingers.