We present atomic-scale force interaction data acquired on an insulating low-symmetry substrate, namely the calcite(10.4) surface. A pronounced asymmetry of the imaged species is apparent along the vertical axis, which will be identified as a tilted band of purely attractive short-range interaction forces. An independent determination of the absolute surface orientation by an optical method suggests that the observed asymmetry is related to the tilt of the carbonate groups within the surface, which, in turn, is linked to the surface orientation. Thus our noncontact atomic force microscopy based work presents the determination of the absolute orientation for a low-symmetry surface.