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.
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