We examined in three experiments whether the perception of surface reflectance in 3-D geometrical shapes is influenced by the mode of lighting, the level of surface reflectance, the number of polyhedral faces, and the regularity of polyhedral shape. As stimuli, we used simulations of regular polyhedra in a 2AFC constant-stimuli procedure to measure how large variations in the reflectance needed to be for observers to be able to tell whether the whole surfaces were uniform or non-uniform. In almost all the cases observers were more successful in discriminating non-uniform polyhedra in the hemispherical diffuse lighting conditions than in the collimated lighting conditions. The different levels of reflectance had no effect on the discrimination of non-uniformity. Second, as the number of faces of the shape increased, discrimination thresholds became lower, indicating that the interpretation of reflectance variations was better when a shape had many faces. Finally, the regularity of the shape, such as the central symmetry, was not an important factor. These results suggest that the interpretation of surface reflectance is more precise when surfaces have less variance in relative strengths between the face luminance values; these surfaces were the ones obtained under hemispherical diffuse lighting.