  We consider 2- and 3-dimensional cubic monocrystalline and polycrystalline
materials. Expressions for Young's and shear moduli and Poisson's ratio are
expressed in terms of eigenvalues of the stiffness tensor. Such a form is well
suited for studying properties of these mechanical characteristics on sides of
the stability triangles. For crystalline high-symmetry directions lines of
vanishing Poisson's ratio are found. These lines demarcate regions of the
stability triangle into areas of various auxeticity properties. The simplest
model of polycrystalline 2D and 3D cubic materials is considered. In
polycrystalline phases the region of complete auxetics is larger than for
monocrystalline materials.
