  Auxetic behavior is a fascinating mechanical property which probably
represents the paradigm of mechanical metamaterials. Despite that nowadays it
is a widely known phenomenon, a fundamental micro-mechanical understanding
which allows the proper control and design of new auxetic material remains
mystified. In this letter we show an important step forward setting a unified
framework for a large class of auxetic materials composed of 2D rotating rigid
units. In addition, a simple pathway for the design of new auxetic material is
established based on three simple rules. In particular, we construct for the
first time exotic crystals, quasi-crystal and isotropic materials with negative
Poisson ratio, which in an ideal design reach the perfect auxetic limit. At the
core of this behavior is a low energy mode reminiscent of a non trivial floppy
mode that exists in the idealized scenario. A natural connection between 2D
rotating rigid auxetic with an antiferromagnetic spin is established which
allows to identify general properties of the material. Finally, we show that
the auxetic response is robust under small perturbation in the design.
