Named shapes a polycule can take — three all connected (triad/throuple), four (quad), or a "V" where one hinge dates two people who aren't dating each other.
Polyamory grew a small vocabulary of shapes because, past two people, "we're dating" stops explaining itself. Draw the connections between everyone and you get a diagram — that's the polycule. Name the common diagrams and you get these four. A triad (colloquially a throuple, from "three" plus "couple") is three people all involved with each other. A quad is four, in some configuration of dating. A vee is the odd one out: not everyone connects.
The vee earns its own line because of the hinge — the person at the point of the V, dating two partners who aren't dating each other. Those two are metamours: linked through a shared partner, not through romance. The hinge carries real weight, juggling two relationships that barely touch and absorbing the fact that a bad week on one arm is felt on the other. It's the most common real-world shape and the least Instagrammable, which tells you something about which ones get photographed.
Here's the part the aesthetic hides: these are descriptions, not destinations. A vee where the two metamours fall for each other becomes a triad; a triad where two people drift becomes a vee. None of them is the "evolved" version of the others, and none is a starter kit for a couple shopping for a third — the shape that gets people burned is exactly that, two treating a whole person as a plus-one. The map is useful. Just don't mistake it for a ranking.