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Auxetic materials are those which exhibit negative Poisson’s ratio, i.e. these solids expand transversely when stretched longitudinally. In recent years the concept of semi-auxetics has been examined for cellular solids based on combination of re-entrant and hexagonal microstructures. In this paper we identify a type of rotating unit that gives positive Poisson’s ratio so that a study can be made on rotating sub-structures that exhibit both positive and negative Poisson’s ratio characteristics. A second type of rotating geometry, whose Poisson’s ratio shifts from negative to positive as stretching increases, has also been identified. Based on kinematical studies we explore the relationship between the on-axis Poisson’s ratios in terms of novel lattice geometry and the magnitude of deformation. [ABSTRACT FROM AUTHOR]