Our tactile perception of external objects depends on skin-object interactions. The mechanics of contact dictates the existence of fundamental spatiotemporal input features—contact initiation and cessation, slip, and rolling contact—that originate from the fact that solid objects do not interpenetrate. However, it is unknown whether these features are represented within the brain. We used a novel haptic interface to deliver such inputs to the glabrous skin of finger/digit pads and recorded from neurons of the cuneate nucleus (the brain’s first level of tactile processing) in the cat. Surprisingly, despite having similar receptive fields and response properties, each cuneate neuron responded to a unique combination of these inputs. Hence, distinct haptic input features are encoded already at subcortical processing stages. This organization maps skin-object interactions into rich representations provided to higher cortical levels and may call for a re-evaluation of our current understanding of the brain’s somatosensory systems.