By enumerating all sequences of length 20, we study the designability of structures in a two-dimensional hydrophobic-polar (HP) lattice model in a wide range of intermonomer interaction parameters. We find that although the histogram of designability depends on interaction parameters, the set of highly designable structures is invariant. So in the HP lattice model the high designability should be a purely geometrical feature. Our results suggest two geometrical properties for highly designable structures; they have the maximum number of contacts and a unique neighborhood vector representation. Also we show that the contribution of perfectly stable sequences in the designability of structures plays a major role in making them highly designable.