The hollow-face illusion, in which a mask appears as a convex face, is a powerful example of binocular depth inversion occurring with a real object under a wide range of viewing conditions. Explanations of the illusion are reviewed and six experiments reported. In experiment 1 the detrimental effect of figural inversion, evidence for the importance of familiarity, was found for other oriented objects. The inversion effect held for masks lit from the side (experiment 2). The illusion was stronger for a mask rotated by 90° lit from its forehead than from its chin, suggesting that familiar patterns of shading enhance the illusion (experiment 2). There were no effects of light source visibility or any left/right asymmetry (experiment 3). In experiments 4 - 6 we used a "virtual" hollow face, with illusion strength quantified by the proportion of noise texture needed to eliminate the illusion. Adding characteristic surface colour enhanced the illusion, consistent with the familiar face pigmentation outweighing additional bottom - up cues (experiment 4). There was no difference between perspective and orthographic projection. Photographic negation reduced, but did not eliminate, the illusion, suggesting shading is important but not essential (experiment 5). Absolute depth was not critical, although a shallower mask was given less extreme convexity ratings (experiment 6). We argue that the illusion arises owing to a convexity preference when the raw data have ambiguous interpretations. However, using a familiar object with typical orientation, shading, and pigmentation greatly enhances the effect.