I know it's silly, trying to categorize the uncategorizable (that is to say life, and especially love!), but it can be engaging to give it a go when you see the same patterns many times over, which I definitely feel like I have, mainly on the Poly Relationships Corner board. My aim in posting this was to see if any others had seen the same patterns, or other patterns.
As with much of what anyone writes, in addition to, or perhaps even more than, describing others, I find that this list is a mirror for myself. When I first got involved with my gf and her husband, I expected a unicorn arrangement. Then I sort of dreamed we could become a serendipitous triad. I let that idea go the way of all unrequited sentiments and have found a fulfilling groove in our heirarchical vee. I wonder if there could ever be space in our lives for an egalitarian vee -- I doubt it, at this point, and I don't need that to ever happen to feel like the relationship is fruitful and worthwhile... but for whatever reason, the possibility of it is important to me, I wouldn't be entirely happy in a situation where I thought that was an impossibility.
I think it would be possible to relate many scenarios back to these rough stabs at categories (ex. "We're sort of an 'inverted' heirarchical vee, in that the partner I started seeing later is the one with whom I have a primary relationship" or "We sort of look like a heirarchical vee on the outside but we function like an egalitarian vee"), but that doesn't mean there's any reason to, and of course there are many 3-person configurations which fall completely outside of these versions of archetypal 2+1 arrangements that I've outlined. And this goes without saying but I'll say it regardless, there are many poly configurations that go beyond three people.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.