Originally Posted by bookbug
We did call it a triad, because we three all loved each other. However, the other woman and I did not share sex, so by strict sexual definition we were a vee. That said, the other female partner and I were the best of friends. She and I had common interests outside of our mutual guy and pursued those together. Loving relationships do not necessarily need a sexual component.
Loving relationships do not need a sexual component, at all. If I have implied something to the contrary, I have misspoke, because the statement is not even remotely true.
However, using the definition you provided, I have a theoretical triad:
Originally Posted by Marcus
I live with my sister and her childhood friend. I love them both deeply, I'd do anything for them. I am not sexual with either of them but we are so close and share many interests - some of them the three of us share and some of them the pairs of us share.
I am in a triad with my sister and her childhood friend.
I have no problem with saying that loving relationships of all kinds can be valued. However, "triad" is a word referring to romantic relationships. Using that word to describe my friendships might be chuckle-worthy, but it is inaccurate.
The OP is talking about romantic relationships and is making an assumption that all involved parties should have sexual connection. That is an assumption which is only relevant in the triad/quad style of relating.