This study contrasted the role of surfaces and volumetric shape primitives in three-dimensional object recognition. Observers (N = 50) matched subsets of closed contour fragments, surfaces, or volumetric parts to whole novel objects during a whole–part matching task. Three factors were further manipulated: part viewpoint (either same or different between component parts and whole objects), surface occlusion (comparison parts contained either visible surfaces only, or a surface that was fully or partially occluded in the whole object), and target–distractor similarity. Similarity was varied in terms of systematic variation in nonaccidental (NAP) or metric (MP) properties of individual parts. Analysis of sensitivity (d′) showed a whole–part matching advantage for surface-based parts and volumes over closed contour fragments—but no benefit for volumetric parts over surfaces. We also found a performance cost in matching volumetric parts to wholes when the volumes showed surfaces that were occluded in the whole object. The same pattern was found for both same and different viewpoints, and regardless of target–distractor similarity. These findings challenge models in which recognition is mediated by volumetric part-based shape representations. Instead, we argue that the results are consistent with a surface-based model of high-level shape representation for recognition.