Science

The Mosuo (a Himalayan Chinese ethnic group) and the Himba (the Namibia and Angola border region) are both very interesting in this respect.

The Mosuo do not have marriage (although their now extinct aristocracy and nearly extinct priesthood did/do). They live in their family home all their lives. Mosuo women have sexual freedom; no one cares how many partners they have or whether there's more than one relationship ongoing simultaneously, and it's not always certain who someone's father is (the matriarchs keep tabs on relationships to help ward off accidental incest). Fathers are not expected to contribute; they raise the children of their sisters and contribute financially to their birth-family household. But, despite the freedom to have many partners on the go with no adverse social consequences at all, most Mosuo tend towards serial monogamy, with some relationships lasting years, others for a lifetime. Those that move to urban China for work tend to adopt traditional marriage because the Mosuo lifestyle is not practical without a whole household to help care for the children.

The Himba, on the other hand, do have marriage and, polyamory for men who are wealthy enough to support more than one wife. But wives are free to have as many other partners as they wish and many women, married or unmarried, will have several on the go at the same time. If a woman wants to sleep with a married man, she gets permission from his wife. Women will often have children before they get married and those they have after marriage are not necessarily fathered by their husbands. It's not an issue because they're herders; children are a source of wealth (more goats can be herded) so the men do not care who the fathers of their children are.

I'm no anthropologist, and I hope I've done these groups justice with my brief descriptions. It's a fascinating topic, especially with respect to polyamory in a rich world context.

Slightly correcting the math here. 2 people is one relationship (AB). 3 people is 3 relationships (AB, AC, BC). Add another person and it's 6 relationships (AB, AC, AD, BC, BD, CD). Add a another person (5th) and it's 10 relationships (AB, AC, AD, AE, BC, BD, BE, CD, CE, DE).

The formula for a relationship with X people is the Sum of all numbers between 1 and X-1,

I'm assuming everyone is bisexual because that's my personal policy in life.

The other "scaling" problem comes in the difference between, on the one hand, a small percentage of people trying to make polyamory work where various combinations exist, and on the other, a society built around normative polygamy or polyandry with associated prestige for those with multiple partners. With the latter, and I'm specifically thinking of Fundamentalist Mormon groups, there is virtually no way to avoid a demographic crisis with various forms of authoritarian awfulness as your only social "band-aids" to keep the practice lurching along.

@SJ_Zero As a poly person myself I thought I'd chime in:

One is a scaling problem. Let’s say you have a couple. Then add one person. Now instead of one relationship, you have three to worry about. Add yet another person, now you have 4 relationships. Add another person, now you have 9. Have each new so get a so, now you have 30.

This rapid geometric growth in relationships presumes that everyone is in a relationship with everyone else within the polycule, and this is not often the case. When you make a friend, it does not imply that you're now in a friendship with everyone else they are friends with. It's the same with polyamorous relationships, many polyamorous people don't care to have a relationship with, or even know their metamours.

The resource thing also hits in other ways. A lot of women want children eventually, and ideally children require resources – space, time, money. In a monogamous relationship, a woman can monopolize a man’s resources, whereas under polyamory she needs to share.

This can work both ways, with a kitchen table/communal living sort of poly situation it can also mean more potential time, resources, and attention per child, with more adults looking out for the children's interests. The, "it takes a village," approach. Potentially more caregivers also means more socialization and oversight. In monogamous nuclear families there's opportunity for abusive situations to arise because of isolation, as only a small number of people truly know what's going on within them. I have a hard time imagining a Mommy Dearest sort of situation in a large poly household when there's a lot of adults around.
Some problems do arise though, especially when it comes to the issues of inheritance and financial support within a largely monogamous legal framework. Moralistic judges may deny custody because a parent chose a non-traditional relationship structure. Then there's the issue of inheritance and property rights, which is baked into monogamy. In fact I believe this is one of the main reasons monogamy is the default today; genetic studies suggest that monogamy might have evolved more recently, less than 10,000 to 20,000 years ago, right around the time we stopped hunter-gathering and switched to agriculture, when social stability was achieved by knowing who gets the farm.

You can split people off and say “hey, I’m going to just have time with girl 1 today and girl 2 tomorrow”, and that can set up a sort of firewall, but there’s a bit of a resource problem there where there’s only 24 hours in a day and someone’s going to feel left out or someone who needs more support won’t get it.

Very true! Love may be infinite but time is not. Scheduling is important and so is making sure everyone feels loved and included, and there's sometimes negotiations to make sure everyone's needs are met.

On the topic of kids, there can be a real problem if a woman gets pregnant. Whose is it?

This is also an issue when dating in a monogamous framework. If it matters, there's paternity testing.

Honestly, you can make it work, but it’s hard mode. It’s much more difficult to make polyamory work than monogamy

I would say it's different, easier in some ways, harder in others. One way it's easier: there isn't so much pressure to be everything to your partner, to meet all their needs or risk being left for someone who does. Instead, you can have partners that fulfill different needs without abandoning the last one. It's like having multiple different friends you do different activities with.
I'd say what makes it more challenging are the additional complications of more personal dynamics to work through; polyamory requires a lot of communication. You can't rest on your laurels or ignore issues, you always have to be maintaining both your relationships and yourself.