  The computation of the numerical index of a Banach space is an intriguing
problem, even in case of two-dimensional real polyhedral Banach spaces. In this
article we present a general method to estimate the numerical index of any
finite-dimensional real polyhedral Banach space, by considering the action of
only finitely many functionals, on the unit sphere of the space. We further
obtain the exact numerical index of a family of $3$-dimensional polyhedral
Banach spaces for the first time, in order to illustrate the applicability of
our method.
