  In this work, we provide a necessary and sufficient condition on a polyomino
ideal for having the set of inner 2-minors as degree reverse lexicographic
Gr\"obner basis, due to combinatorial properties of the polyomino itself.
Moreover, we prove that when the latter holds the ideal coincides with the
lattice ideal associated to the polyomino, that is the ideal is prime. As an
application, we describe two new infinite families of prime polyominoes.
