Off topic but I've always hated the argument that "polyamory" is somehow a messed-up word because it's from both Latin and Greek roots. Big deal...so is the word "television," and that's kind of stuck.
Back on subject, I don't know of a word that described my last poly relationship: two halves of a couple both in a relationship with one other person, but that person's partner not involved in the relationship. It isn't quite a quad, and "triad-and-one" doesn't seem to cut it.
Well, you three were in a triad. And there are 3 dyads in a triad. And your shared partner was also in another dyad. And their partner was your metamour.
Well, you three were in a triad. And there are 3 dyads in a triad. And your shared partner was also in another dyad. And their partner was your metamour.