Usotsuki na Gemini

Aoi and Rin are twins who are very close to each other. Aoi is a tomboy who is also a big kendo nut while Rin is a budding designer. Aoi, after losing a fight against a former acquaintance, Izumi, decides to hunt him down for a rematch but somehow Rin doesn't like the idea? What does he really see her as?