A framework is outlined in which individual faces are assumed to be encoded as a point in a multidimensional space, defined by dimensions that serve to discriminate faces. It is proposed that such a framework can account for the effects of distinctiveness, inversion, and race on recognition of faces. Two specific models within this framework are identified: a norm-based coding model, in which faces are encoded as vectors from a population norm or prototype, and a purely exemplar-based model. Both models make similar predictions, albeit in different ways, concerning the interactions between the effects of distinctiveness, inversion and race. These predictions were supported in five experiments in which photographs of faces served as stimuli. The norm-based coding version and the exemplar-based version of the framework cannot be distinguished on the basis of the experiments reported, but it is argued that a multidimensional space provides a useful heuristic framework to investigate recognition of faces. Finally, the relationship between the specific models is considered and an implementation in terms of parallel distributed processing is briefly discussed.