  We propose a class of auxetic three-dimensional lattice structures. The
elastic microstructure can be designed in order to have omni-directional
Poisson's ratio arbitrarily close to the stability limit -1. The cubic behavior
of the periodic system has been fully characterized; the minumum and maximum
Poisson's ratio and the associated principal directions are given as a function
of the microstructural parameters. The initial microstructure is then modified
into a body centered-cubic system that can achieve a Poisson's ratio lower than
-1 and that can also behave as an isotropic three-dimensional auxetic
structure.
