The essential midline symmetry of human faces is shown to play a key role in facial coding and recognition. This also has deep and important connections with recent explorations of the organization of primate cortex, as well as human psychophysical experiments. Evidence is presented that the dimension of face recognition space for human faces is dramatically lower than previous estimates. One result of the present development is the construction of a probability distribution in face space that produces an interesting and realistic range of (synthetic) faces. Another is a recognition algorithm that by reasonable criteria is nearly 100% accurate.