Story with a multidimensional girl

I believe this was a childrens book. I would have read it about 10 years ago.

The main character was a girl who could change her appearance when concentrating on herself in the mirror. This is later explained as her shifting around in more than three dimensions. She at some point tries to point at something she sees in a higher dimension, and another character says her arm turns red and disappears. She at one point finds a hypersphere that she can "fold" into higher or lower dimensions that she carries around with her which helps her use her powers.

She is part of a group of four children with different such power that start out trapped in a house and unaware of their powers and origins. They work differently, one boy turns into a metallic dragon-like creature and is then semi-killed/reborn via magic bacteria/nanomachines.

Answer

The series you are speaking of is the Chronicles of Chaos series. In specific you are talking about Orphans of Chaos

In addition to the characters you mention, another is a magician and the other is a psychic. And apparently we both forgot a fifth?

It turns out that the girl's powers naturally trump the dragon boy's, whose trumps the magician's, whose trumps the psychic's, whose trumps hers.

They eventually defeat the people who run the school.

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