Character Analysis
Antiochus's daughter is the play's "sinful" princess. She's smokin' hot, she's got a rich dad, and dudes come from all over the world for a chance to marry her.
Here's how Gower describes her: "So buxom, blithe, and full of face / As heaven had lent her all his grace" (1.23-24). Okay. We get it: she's mostly known for her beauty. That must be why Shakespeare doesn't give her a proper name—the girl has got no personality or identity of her own, aside from being her father's daughter... and lover.
Oh, yeah: did we mention that Antiochus's daughter has a dirty little secret? The first thing we learn in this play is that she's been schtupping her dad. Not only that, but the incestuous relationship has gone on for so long that she doesn't even see anything wrong with it. According to Gower, this makes her a "bad child" (1.Prologue.27-28).
So, we know what you might be thinking: are we really supposed to get all Judge Judy on Antiochus's daughter like Gower does? Aren't parents supposed to look out for their kids and take care of them? If this were real life, Antiochus's daughter would be a victim, and her dad would be locked up behind bars. Check out how Gower describes what happened:
With whom the father liking took,
And her to incest did provoke. (1.25-26)
In other words, her father seduced her and "provoke[d]" her into the relationship. Okay, we're not going to get into an argument with Shakespeare about whether that is even possible. The point the play seems to be making is that the princess was just bad to begin with, and the fact that she's in an incestuous relationship with her dad is just proof of that. It's not the incest that makes her and her father bad; it's their badness that makes them think it's okay to get all incesty.
That's probably why the gods send down a bolt of fire from the heavens and burn her and Antiochus to a crisp while they're out joyriding in their chariot (2.4.6-12).