Mine's not math, but chemistry. Equally geeky, but in a different direction.
I was thinking that lots of poly people use letters to describe their relationships (V or N or W). But there are a lot of configurations that just doesn't work for. So I had a flash of brilliance. Assume each person is a carbon atom in a hydrocarbon. Use organic nomenclature. So a V is a propane. A triad becomes cyclopropane. Okay, so if you want to stick with actual molecules, each person would be limited to four partners, but love doesn't care whether carbon has five bonds.
Okay, I'm finished with my moment of geek. Continue onwards with your math.