*waves hand* Fellow poly person here.
"Triad" in the poly community has an additional meaning that it refers to all three people in the relationship being involved with one another. I am currently (well, with the people in my house) in a V relationship -- my partner Morgan is involved with me, and my girlfriend Grey is involved with me, but while they are both close friends, they are not romantically or intimately involved with each other. That is something that is not entirely obvious to people outside the poly community.
You say you've decided to just refer to it as a relationship, and that is perfectly acceptable too! My particular type of poly is known as "network" poly. My partner and girlfriend in my home have no other relationships, but my long-distance girlfriend is married and handfasted to whom I refer to as her Other Husband, and they have their own relationships, too... network fits best because there's a long string of connections and metamours (a metamour is somebody that your partner has a relationship with but you do not -- so my girlfriend's husbands would be metamours).
Needless to say, all of this, while makes sense in the context of the poly community, is not something that often comes into play in day to day society. So, for simplicity's sake, I (and many other poly folk) just refer to ourselves as having a poly relationship, and explain further as needed.