  We propose a novel two-dimensional hierarchical auxetic structure consisting
of a porous medium in which a homogeneous matrix includes a rank-two set of
cuts characterised by different scales. The six-fold symmetry of the
perforations makes the medium isotropic in the plane. Remarkably, the mesoscale
interaction between the first- and second-level cuts enables the attainment of
a value of the Poisson's ratio close to the minimum reachable limit of -1. The
effective properties of the hierarchical auxetic structure are determined
numerically, considering both a unit cell with periodic boundary conditions and
a finite structure containing a large number of repeating cells. Further,
results of the numerical study are validated experimentally on a polymeric
specimen with appropriately arranged rank-two cuts, tested under uniaxial
tension. We envisage that the proposed hierarchical design can be useful in
numerous engineering applications exploiting an extreme auxetic effect
