Previous investigations of the neural code for complex object shape have focused on two-dimensional pattern representation. This may be the primary mode for object vision given its simplicity and direct relation to the retinal image. In contrast, three-dimensional shape representation requires higher-dimensional coding derived from extensive computation. We found evidence for an explicit neural code for complex three-dimensional object shape. We used an evolutionary stimulus strategy and linear/nonlinear response models to characterize three-dimensional shape responses in macaque monkey inferotemporal cortex (IT). We found widespread tuning for three-dimensional spatial configurations of surface fragments characterized by their three-dimensional orientations and joint principal curvatures. Configural representation of three-dimensional shape could provide specific knowledge of object structure to support guidance of complex physical interactions and evaluation of object functionality and utility.