There is a third possible structure, but it is not stable and has never been shown to exist. Each of the oxygens is single-bonded to the other two oxygens, forming a triangle.
Notice how I used an equilibrium-type arrow between the two structures. Some people misinterpet this to mean the actual molecule shifts back and forth between the two structures.
IT DOES NOT!!!!!!!
The actual molecule is stable and unchanging in the above sense. The actual molecule exists in an equilibrium state and NONE of the resonance structures capture the real molecule.