  We consider the nonclassicality distance indicator of a state in
finite-dimensional quantum systems which is evaluating a state nonclassicality
by its remoteness from the set of "classical states". The latter are identified
with those states whose Wigner function is non-negative. The corresponding
Wigner function's positivity polytope in the simplex of qudit eigenvalues is
introduced and the representation for the nonclassicality distance indicator as
a piecewise function is derived. The results are exemplified by the qutrit
case.
