In my understanding (and I could be wrong), being in an "open relationship" and polyamory" are two different things.
Polyamory and open relationships are both forms of consensual non-monogamy, but they differ in key ways:
Both relationship styles require clear communication, consent, and boundaries to be healthy and successful and to be honest it sounds like he wans is cake and to eat it. What's good for the goose is apparently not good for the gander and realistically speaking, you are the one that is conventionally free to do as you wish, not him.
Polyamory
Emotional and Romantic Connections: In polyamory, individuals have multiple romantic and emotional relationships simultaneously. These relationships are often deep and meaningful, with the consent and knowledge of all involved. And I'm not sure his wife knows about you - as would be the norm.
Commitment: People in polyamorous relationships may have multiple partners with whom they share a significant level of commitment and emotional intimacy.
Types: There are various forms of polyamory, such as hierarchical polyamory (where there are primary and secondary partners), solo polyamory (where individuals maintain their independence), and kitchen table polyamory (where all partners are comfortable interacting with each other).
Open Relationships
Physical Connections: Open relationships typically involve a primary couple who are emotionally committed to each other but allow for sexual relationships with other people.
Casual Nature: These external relationships are usually more casual and focused on physical intimacy rather than emotional bonds.
Primary Partnership: The primary relationship remains the central focus, with external relationships being secondary and less emotionally involved.
Both relationship styles require clear communication, consent, and boundaries to be healthy and successful.
Its pretty obvious your wants and needs are different and to be honest, given you have also have suspicions his wife is not aware of his unfaithfulness, just walk away. Getting involved with a married man when deep feelings are in volved is one thing, but potentially destroying a women and kids lives for a bit of non committal fun is not something you need to get involved with, there are plenty of men out there who are free to go this route. Don't get me wrong if he is lying, his chickens will come home to roost, but if you want a stress free time so you can concentrate on your PHD, the shit that can unfurl when dating a married man, is not something you should knowingly be contemplating.
You, and his wife and kids deserve better.