In four experiments, subjects examined four categories of rotating eight-vertex geometric forms in parallel projection. Some of the figures appeared to deform, even though rigid three-dimensional interpretations were possible mathematically. Our results from several deformation-rating tasks indicated that most of the configurations maintained a rigid appearance throughout their rotations, although one category of stimuli appeared to deform more frequently than the others. Configurations from the category that contained a high proportion of stimuli that appeared to deform were also shown to be more difficult to discriminate from stimuli that had no rigid three-dimensional interpretation (measured using a signal detection task). To account for these findings, a theory was formulated based on the use of monocular depth cues in the perception of shape. Static monocular depth cues we define as those which are present in non-moving stimuli and Dynamic monocular depth cues are those that are only present in moving stimuli. We conclude that static cues dominate the perception of shape when humans respond to parallel (and, most likely, polar) projections of rotating objects with rigid three-dimensional interpretations. Further, subjects cannot respond to the motion or acceleration profile of part of such a stimulus without responding to the figure as a whole.