Choices have consequences, and it's possible that you've lost her for good. Whether you can repair the broken trust between you depends on many things -- for example, the formality of commitment between you two, the length of your relationship, was the cheating a one-time tryst or a longer affair, who it was with (hopefully, not her best friend!), and the emotional baggage in both your relationship and her past.
If she won't discuss the matter with you in person or via FaceTime, try writing a letter with a heartfelt apology -- yes, the old-fashioned handwritten kind. Perhaps include it in a card or have a florist deliver it along with a dozen roses. People don't write letters anymore, and it takes an investment of time and heart, so you'll get her attention. Mail it if to her, if needed.
You get ONE shot at this so make it good. Don't make excuses or give any justifications or rationales. Own how wrong you were and express how you let both her and yourself down. In your own words, validate how cheating must have made her feel (second best, unwanted, rejected!). Remember that emotional cheating and physical cheating both hurt like hell. Tell her WHY she is the only one for you and why you realize that now that she isn't in your life. Paint the picture of where you want the relationship to go, any dreams you have for the two of you, and (if it's true) say that you're willing to do the hard work to rebuild her trust if she gives you another chance. Be warned that this involves answering a lot of questions about the cheating, a lot of anger and tears, and having to account for your whereabouts.
Don't expect instant forgiveness, even under the best of circumstances. Why? One of the great relationship insecurities is whether a partner will continue to be faithful when one's good looks fade, health or wealth declines, luck turns sour, or they're at their most vulnerable. She probably questions that if you cheated now why you wouldn't do it again?
You own causing her this pain. Spill your guts, then tell her the decision is all hers if she wants to take it slow and try to work it out. Then, if her answer is no, stop. That's unwanted attention. Chalk it up to a lesson learned the hard way.