The ability of primates to effortlessly recognize faces has been attributed to the existence of specialized face areas. One such area, the macaque middle face patch, consists almost entirely of cells that are selective for faces, but the principles by which these cells analyze faces are unknown. We found that middle face patch neurons detect and differentiate faces using a strategy that is both part based and holistic. Cells detected distinct constellations of face parts. Furthermore, cells were tuned to the geometry of facial features. Tuning was most often ramp-shaped, with a one-to-one mapping of feature magnitude to firing rate. Tuning amplitude depended on the presence of a whole, upright face and features were interpreted according to their position in a whole, upright face. Thus, cells in the middle face patch encode axes of a face space specialized for whole, upright faces.