The discovery that deep convolutional neural networks (DCNNs) achieve human performance in realistic tasks offers fresh opportunities for linking neuronal tuning properties to such tasks. Here we show that the face-space geometry, revealed through pair-wise activation similarities of face-selective neuronal groups recorded intracranially in 33 patients, significantly matches that of a DCNN having human-level face recognition capabilities. This convergent evolution of pattern similarities across biological and artificial networks highlights the significance of face-space geometry in face perception. Furthermore, the nature of the neuronal to DCNN match suggests a role of human face areas in pictorial aspects of face perception. First, the match was confined to intermediate DCNN layers. Second, presenting identity-preserving image manipulations to the DCNN abolished its correlation to neuronal responses. Finally, DCNN units matching human neuronal group tuning displayed view-point selective receptive fields. Our results demonstrate the importance of face-space geometry in the pictorial aspects of human face perception.