  Auxetic materials are characterized by a negative Poisson's ratio,
$\mathrm{\nu}$. As the Poisson's ratio becomes negative and approaches the
lower isotropic mechanical limit of $\mathrm{\nu = -1}$, materials show
enhanced resistance to impact and shear, making them suitable for applications
ranging from robotics to impact mitigation. Past experimental efforts aimed at
reaching the $\mathrm{\nu = -1}$ limit have resulted in highly anisotropic
materials, which show a negative Poisson's ratio only when subjected to
deformations along specific directions. Isotropic designs have only attained
moderately auxetic behavior, or have led to structures that cannot be
manufactured in 3D. Here, we present a design strategy to create isotropic
structures from disordered networks that leads to Poisson's ratios as low as
$\mathrm{\nu = -0.98}$. The materials conceived through this approach are
successfully fabricated in the laboratory and behave as predicted. The
Poisson's ratio $\mathrm{\nu}$ is found to depend on network structure and bond
strengths; this sheds light on the structural motifs that lead to auxetic
behavior. The ideas introduced here can be generalized to 3D, a wide range of
materials, and a spectrum of length scales, thereby providing a general
platform that could impact technology.
