I hate my phone... I had all of this typed out and then it crashed and it was all gone. I guess, I'll try it again:
Being polyamorous just means you can be attracted to or even love multiple people at the same time. That does not necessarily mean you have multiple relationships side by side, it doesn't necessarily mean you even have something else on the side, and it doesn't necessarily mean it's not cheating. It all comes down to communication. As long as everybody involved knows what's going on and accepts it it isn't cheating. What that means can differ wildly from relationship to relationship. Sometimes it can mean you have multiple equal relationships to different people - even different families perhaps, sometimes it can mean there are just more than two people in the same relationship together - but that's rarer than you might think, sometimes it can mean one partner is ok with the other one having sex outside of their relationship but nothing serious, some couples decide it's only ok if they both do it, some couples are ok with inviting people in but not with either partner doing their own thing, sometimes it can mean one person is ok with their partner having sex outside of their relationship as long as it's the opposite sex of what they have at home, and sometimes partners might not be ok with any of it. It's all about what you both (or more) have accepted together.
And lastly, - this is where my phone crashed last time - even though many people have used polyamory as an excuse for cheating or as an argument that they infact didn't cheat, cheating is a completely seperate issue. Being polyamorous doesn't mean you always need to have multiple partners at the same time. So you can still be in a monogamous relationship if that person is just more important to you than having multiple partners. And, of course, when you do have multiple partners it can certainly be cheating if it's not what you agreed on. If I may quote Samm Levine: "Cheating is when one person does something they know in their heart the other person wouldn't want them to do."