  Dilational materials are stable three-dimensional isotropic auxetics with an
ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and
characterize crystalline metamaterials approaching this ideal. To reveal all
modes, we calculate the phonon band structures. On this basis, using cubic
symmetry, we can unambiguously retrieve all different non-zero elements of the
rank-4 effective metamaterial elasticity tensor, from which all effective
elastic metamaterial properties follow. While the elastic properties and the
phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes
isotropic and approaches -1 in the limit of small internal connections. This
finding is also supported by independent static continuum-mechanics
calculations. In static experiments on macroscopic polymer structures
fabricated by three-dimensional printing, we measure Poisson's ratios as low as
-0.8 in good agreement with theory. Microscopic samples are also presented.
