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Despite their outstanding mechanical properties, with many industrialapplications, a rational and systematic design of new and controlled auxeticmaterials remains poorly developed. Here a unified framework is established todescribe bidimensional perfect auxetics with potential use in the design of newmaterials. Perfect auxetics are characterized by a Poisson's ratio $\nu=-1$over a finite strain range and can be modeled as materials composed of rotatingrigid units. Inspired by a natural connection between these rotating rigidunits with an antiferromagnetic spin system, here are unveiled the conditionsfor the emergence of a non-trivial floppy mode responsible for the auxeticbehavior. Furthermore, this model paves a simple pathway for the design of newauxetic materials, based on three simple steps, which set the sufficientconnectivity and geometrical constraints for perfect auxetics. In particular, anew exotic crystal, a Penrose quasi-crystal and the long desired isotropicauxetic material are designed and constructed for the first time. Using 3Dprinted materials, finite element methods and this rigid unit model, theauxetic behavior of these designs is shown to be robust under smalldisturbances in the structure, though the Poisson's ratio value relies onsystem's details, approaching $-1$ close to the ideal case.

Auxetic behavior on demand: a three steps recipe for new designs