  We show that two-dimensional band insulators, with vanishing bulk
polarization, obey bulk-and-edge to corner charge correspondence stating that
the knowledge of the bulk and the two corresponding ribbon band structures
uniquely determines the fractional part of the corner charge irrespective of
the corner termination. Moreover, physical observables related to macroscopic
charge density of a terminated crystal can be obtained by representing the
crystal as collection of polarized edge regions with polarizations $\vec
P^\text{edge}_\alpha$, where the integer $\alpha$ enumerates the edges. We
introduce a particular manner of cutting a crystal, dubbed "Wannier cut", which
allows us to compute $\vec P^\text{edge}_\alpha$. We find that $\vec
P^\text{edge}_\alpha$ consists of two pieces: the bulk piece expressed via
quadrupole tensor of the bulk Wannier functions' charge density, and the edge
piece corresponding to the Wannier edge polarization---the polarization of the
edge subsystem obtained by Wannier cut. For a crystal with $n$ edges, out of
$2n$ independent components of $\vec P^\text{edge}_\alpha$, only $2n-1$ are
independent of the choice of Wannier cut and correspond to physical
observables: corner charges and edge dipoles.
