Date of birth: 1984-06-15 
Height: 185cm
Kai is Ichika's other tutor. He teaches her math and science. He is introduced as the twin brother of Sei. Of the two, Kai seems the more extroverted one and more physical in nature and seems to have developed feelings for his twin brother, Sei.  (from Wikipedia)

On the last day of the school year, 14-year-old Ichika Tachibana comes across an old, busted mirror in an unused campus building. When Manatsu, a mysterious girl from inside the mirror, steps out and offers her friendship for the summer, she also offers Ichika magical powers. Now, Manatsu must help Ichika unlock the powers of the 12 Djinn in order to complete her magic training... but perhaps this is something that will prove too difficult a task. Some offers may appear to be too good to be true and this one just may turn out to do more harm than good.
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(Source: Anime News Network)

It's now winter in Kamakura. When Satsuki tells her friends that she'd seen Manatsu, Ichika at first doesn't believe it. But on the day before her 15th birthday, Manatsu's mirror fragment inside Ichika's desk drawer mysteriously disappears. That evening, a young girl calling herself "Mafuyu, Manatsu's identical twin" appears before Ichika with a mischievous smirk on her face.<br><br>
(Source: AniDB)

On the last day of the school year, 14-year-old Ichika Tachibana is on cleaning duty and gets the daunting task of cleaning a huge mirror. As she cleans, a mysterious girl named Manatsu comes out of the mirror and asks for some homework help... and ends up granting Ichika magical powers for the summer! But these powers come with a price, and both of the girls will learn that before summer's end.

Kai Toudou