  We study a frustrated two-dimensional array of dipoles forming an artificial
rectangular spin ice with horizontal and vertical lattice parameters given by
$a$ and $b$ respectively. We show that the ice regime could be stabilized by
appropriate choices for the ratio $\gamma \equiv a/b$. Our results show that
for $\gamma \approx \sqrt{3}$, i.e., when the center of the islands form a
triangular lattice, the ground state becomes degenerate. Therefore, while the
magnetic charges (monopoles) are excitations connected by an energetic string
for general rectangular lattices (including the particular case of a square
lattice), they are practically free to move for a special rectangular lattice
with $\gamma \approx \sqrt{3}$. Besides that, our results show that for $\gamma
> \sqrt{3}$ the system is highly anisotropic in such a way that, even for this
range out of the ice regime, the string tension almost vanishes along a
particular direction of the array. We also discuss the ground state transition
and some thermodynamic properties of the system.
