Cal can only refer to the Obscure Object with literary and pop culture references at first. He describes her freckled skin by quoting Gerard Manley Hopkins: "Glory be to God for dappled things" (3.6.26), and he gets the nickname the Obscure Object from a film. Meanwhile, the Object herself is as far from literary and lyrical as you can get. Her first line of dialog is a belch followed by the catchphrase Bart Simpson has made famous, "Ay, carumba!" (3.6.27)… Stay classy, girl.
Calliope and the Object become friends during a school play, and they become more than friends during a fateful vacation they take to the Object's summer home. Like most first loves, the Object serves as a defining moment in Cal's life, for both good and bad. Sure, she helps Calliope explore her budding sexuality, but she does it in such a cold, detached manner that it lends a veil of shame to the act. Maybe it's not such a bad thing that this relationship ends badly.
Calliope doesn't just explore her budding sexuality with the Object, though—she also pokes around with the Object's brother, Jerome (the Stephanideses are always keeping it in the family, it seems). Both the Object and Jerome are similar: they share a body type, skin color, hair color (except Jerome dyes his hair black), and even personality traits. The fact that Calliope lusts after the Object proves that she is more attracted to females than males—when she has her brief sexual encounter with Jerome, all she can do is think about the Object nearby.
While Calliope is regretfully getting it on with Jerome, the Object is making out with Rex Reese. She swears that she kept it PG-13, but we're not so sure. Maybe she just doesn't want to hurt Calliope's feelings. After all, she seems awfully jealous when she accuses Cal of being "a total slut" (3.9.8). Eventually they make up, but their relationship isn't ever the same.
We have a hard time telling if the love between Calliope and the Object is a one- or two-way street. Cal recalls, "It was never my turn with Object" (3.8.125), and he has a good point. While they're experimenting sexually, the Object pretends to be asleep the whole time, but she also does reciprocate. What do you think the Object would say if asked to articulate her feelings for Calliope?