Symbolism, Imagery, Allegory
Jason has his coin that turns into a sword, and Leo has his magic tool belt. Piper, however, gets a dagger that once belonged to Helen of Troy, the ancient Greek beauty who ran away from her husband with the Greek hero Paris, causing the Trojan War. The blade is called Katoptris, or mirror—because, Annabeth tells Piper, Helen never used it for anything else.
Piper is no Helen, though, and uses the dagger to fight. She cuts up some Earthborn, for example, during the fight with the giant Enceladus. She's also not particularly vain or interested in looking at her reflection—on the contrary, she is irritated and depressed when Aphrodite casts a spell on her to make her super glamorous. And unlike Helen, Piper doesn't betray a love—instead she's horrified when she learns that it's a "rite of passage" for Aphrodite's children to "Break someone's heart on purpose" (15.79-80).
So, given that Helen of Troy doesn't seem to have much to do with Piper, what's with the knife? What's it supposed to symbolize?
We don't think there's a good answer. The connection may be loose, based solely on the fact that Helen of Troy is a beautiful woman associated with love, and Piper is a beautiful woman who is the daughter of the goddess of love. In fact, it seems almost insulting to Piper to link her to Helen, and odd to give her a weapon that is used more for admiring oneself than for battle (even if Piper does use it in battle). You could say that Piper is repurposing Helen's legend—turning vanity to bravery. But why should she have to deal with Helen's legacy in the first place?
Perhaps, then, the dagger symbolizes not Piper's or Helen's shallowness, but the shallowness of the novel. As we discuss in the symbolism section on gods, the straightforwardness of the symbols in The Lost Hero can be enjoyable and satisfying in a lot of ways. But, as Katoptris shows, it can also be irritating. Piper gets linked to Helen of Troy for superficial reasons that make less sense the more you look at them. Piper deserves a better weapon. Give that girl a light-saber.