Abstract: Crystallization is ubiquitous in nature and semicrystalline polymers are of crucial importance in our daily life. Because of their long chain nature, polymers crystallize via a complex pathway, leading to profound metastable states and morphologies. This talk will focus on polymer crystals whose shape is incommensurate with three-dimensional translational symmetry. Examples are helix, hollow tubes and spheres. Not only can this shape-symmetry incommensurateness arise from the intrinsic characteristics of the crystal such as unbalanced chain folding and/or local stress, it also can be imparted by nanoscale confinement. Both cases will be discussed, and emphasis will be given to the formation mechanism, associated properties and possible applications of these unique polymer single crystals.