Worth noting that "Harem", and "Reverse-Harem", "Polyandry", and "Polygamy" all mean a whole bunch of people connected to a single person, just with different connotations about the strength of the connection (unspecified or ownership, vs state & religion approved marriage).
Polyamory does not specify the shape of the polycule at all. In my relationship, I am a transfemme plural lesbian, married to a non-binary person, dating a woman who is in turn married to a man and dating two other men and a non-binary masc person. My metas are not connected to me directly, nor are they to my spouse. I am also in multiple distinct relationships with another plural person whose members have many gender identities. We all care about each other, but each relationship between and around is separately negotiated, so long as the polycule as a whole is made aware of our shape and extent, and we're all protecting each other from the emotional and physical risks we might bring to the table to the best of our ability.
This is a valid polyamory configuration because all configurations are valid polyamory configurations. It doesn't fit any of the other available tags.
And yeah, none of it is cheating, but cheating still conceptually could happen in my irl polycule, because making each other aware of, and protecting each other from, new physical and emotional connections and risks is a requirement.
If someone slept with a person nobody else was aware of, and they intentionally tried to keep it from the rest of us, that'd be cheating; a betrayal of the polycule and all of our relationships within it. It's not that anyone or us would say no, it's that if they're worried about the risks to us enough to want to hide it, they almost certainly shouldn't be doing it without at least processing it first, and one would hope they'd feel comfortable enough with one of the rest of us to do that process with us. If they're not worried about any risk, it shouldn't really be a problem to tell us.
Harems and Polygamy are not equal relationships, they are timeshares on monogamy.