  Motivated by the recent interest in the possible ordering of the CH$_3$NH$_3$
dipoles in the material CH$_3$NH$_3$PbI$_3$, we investigate the properties of
domain boundaries in a simple cubic lattice of dipoles. We perform numerical
simulations in which we set the boundary conditions such that the dipoles at
opposite sides of the simulated sample are ordered in different directions,
hence simulating a domain boundary. We calculate the lowest energy
configuration under this constraint. We find that if we consider only
dipole-dipole interactions the dipole orientations tend to gradually transform
between the two orientations at the two opposite ends of the sample. When we
take into consideration the finite spatial size of the CH$_3$NH$_3$ molecules
and go beyond the point dipole approximation, we find that the domain boundary
becomes sharper. For the parameters of CH$_3$NH$_3$PbI$_3$, our results
indicate that the optimal energy structure has a boundary region of a width on
the order of a single unit cell.
