Zettai Shougeki ~Platonic Heart~

The story centers on the Platonic Heart, a jewel that—according to an old urban legend—can grant any wish when collected. Only a chosen few are allowed to compete in the Platonic Heart hunt. The protagonist is Natsume Honma, who throws herself into the Platonic Heart combat after discovering that her best friend Aya has also been selected as one of the Maidens.