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Auxetics display the anomalous property of expanding laterally when uniaxially stretched, that is, a negative Poisson's ratio, a property that arises from 1) the presence of specific geometric features within the nano/macrostructure of the material and 2) amenable deformations in response to the applied stimulus. Herein, how ancient symmetrical esthetic artifacts have been transformed to functional auxetics through mechanisms that have ripened the field of "mechanical metamaterials" and "architected materials" in the last decades is explored. In particular, the important role and various implementations, both in 2D and 3D, of "rotating rigid units," which range from "rotating squares" to much more complex renditions at various scales of structure, are looked at. The role of rotating rigid units to generate negative thermal expansion and negative compressibility is also delved into. [ABSTRACT FROM AUTHOR]