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Several things will become apparent when Isotte possesses the unicorn.
Her senses are different from a human's. She sees a different set of colors, and in almost all directions at once. She can easily smell the other students behind them and some of their possessions, and can distinguish nuances in those scents which would be undetectable to a human. And, in the same way that she can feel the position of her limbs, she can perceive the current state of her horn in some complex manner distinct from its shape, its position, or anything else she has previously been able to perceive.
Similarly, she can perceive the illusion around her body.
The "unicorn" is much less like the traditional image of a unicorn than she appeared. She is a one-horned quadruped. But underneath an illusion of a pony-like body and straight, spiraled horn, her real body has an exoskeleton, a curved horn, and insect-like wings.