Well, the more basic question there is "what do you mean when you say 'particle?'"
Consider that the word "particle" may be only a poor analogy made in an attempt to make something that is far more complex and subtle at least somewhat understandable.
There are no contradictions, it's true. Therefore an photon is neither a "particle" nor a "wave," but rather is, quite simply, a photon which behaves precisely as a photon behaves.
May be. However it seems to me that even the term “photon” as a descriptor of some third item is itself just a poor attempt to describe something that cannot be described. I think science has at bottom the futile attempt to solve the scientifically unsolveable problem of eternity — in space, size, mass and time. Despite all the collected observations throughout history science has moved not an inch closer to figuring out eternity in any of its dimensions. It has, however, helped society immensely in the material/technological realm.