People can usually recognize a familiar shape independently of its orientation in three-dimensional space. I suggest in this article that they do this by extracting a description of the shape that is frameindependent, or independent of any coordinate system. Such a description is usually sufficient to locate the stored representation of the shape uniquely in long-term memory. However, a frameindependent description does not discriminate mirror-image shapes, which could explain the strong tendency to treat mirror images as equivalent in shape. Once a shape is identified, information about its internal axes (e.g., its top and bottom) can be recovered from memory, so that its orientation relative to the observer can be determined. The shape can then be mentally rotated to its normal or upright orientation; this normative transformation appears to be necessary if the shape is to be distinguished from its mirror image.As freely moving organisms in a world of movable objects, we are faced continually with the problem of recognizing objects or shapes in varying orientations. This is part of the more general problem of pattern recognition, whereby we recognize patterns as invariant despite the fact that they may present themselves to our senses in an infinite variety of manifestations. We may recognize a particular person, for example, whether that person is near or far, standing or sitting, in left or right profile, laughing or crying, in sunshine or in shadow.It is convenient to distinguish properties that are intrinsic to the pattern itself and that serve to define that pattern from those that depend on the particular circumstances under which the pattern is manifest to the observer. We may identify these properties as invariant and circumstantial properties, respectively.That is, we identify what things are by identifying their invariant characteristics, and we also perceive something of the circumstances surrounding them. We recognize a dog, say, but we also perceive where it is in relation to ourselves, what it is doing, and so forth.For most purposes orientation can be considered a circumstantial property. Common movable objects can appear in any orientation, yet we can usually recognize them for what they are. At the same time we can also perceive the orientations they are in. In some cases, however, it is not easy to identify patterns in unusual orientations. Rock (1973) pointed out, for instance, that it is peculiarly difficult to recognize familiar faces if they are upside down, and that it is also difficult to read cursive script upside down. These observations illustrate a further point about pattern recognition, namely, that it is hierarchical; one may still recognize an upside-down face as a face, even though