  We investigate the spin and charge densities of surface states of the
three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum
description of the material [Zhang {\em et al.}, Nat. Phys. 5, 438 (2009)]. The
spin structure on surfaces other than the 111 surface has additional complexity
because of a misalignment of the contributions coming from the two sublattices
of the crystal. For these surfaces we expect new features to be seen in the
spin-resolved ARPES experiments, caused by a non-helical spin-polarization of
electrons at the individual sublattices as well as by the interference of the
electron waves emitted coherently from two sublattices. We also show that the
position of the Dirac crossing in spectrum of surface states depends on the
orientation of the interface. This leads to contact potentials and surface
charge redistribution at edges between different facets of the crystal.
