  The orientation of a rigid object can be described by a rotation that
transforms it into a standard position. For a symmetrical object the rotation
is known only up to multiplication by an element of the symmetry group. Such
ambiguous rotations arise in biomechanics, crystallography and seismology. We
develop methods for analyzing data of this form. A test of uniformity is given.
Parametric models for ambiguous rotations are presented, tests of location are
considered, and a regression model is proposed. A brief illustrative example
involving orientations of diopside crystals is given.
