Is it a bad idea to contact this ex of mine?

Three years ago, I cheated on my boyfriend of four years. He found out and after a short period of uncertainty, we broke up. We tried to see each other and remain friends, but eventually one day he just stopped talking to me (aka "ghosted" me). Since that day we have never spoken again. When I have seen him in public since then, he didn't acknowledge me. I accept full responsibility for what I did, and it was the worst mistake of my life. I could never do that again. I hurt him and myself quite a lot as well by ruining the relationship... and in one way it is worse to know my suffering was entirely because of my own actions. It isn't constant, but I have never stopped thinking about it, and wanting to talk to him just one more time (to tell him I'm sorry, to thank him for the person he was to me for the four years we dated etc). Closure, really. He was the most important person I ever had in my life and I want to be able to get some of these feelings off of my chest? Is there any way I can do this that is acceptable or should I not contact him?
Is it a bad idea to contact this ex of mine?
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