Cube Route by Piers Anthony

The provided text follows Cube, a woman on a quest to become beautiful, who is advised by the Good Magician Humfrey to find a route to Counter Xanth, a new, inverted territory. Accompanied by her ever-present, sarcastic demoness companion, Metria, and a growing party of unique individuals stored in a magic pouch, Cube navigates fantastical landscapes filled with puns and unexpected challenges. Her journey leads her through various magical realms and even into Mundania, where she temporarily inhabits another woman's body, ultimately learning that inner strength and gumption are more valuable than outward appearance, leading to a surprising transformation and the successful completion of her mission.