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Alexandre V. Borovik, Anna Borovik, "Mirrors and Reflections: The Geometry of Finite Reflection Groups"

Mirrors and Reflections is a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups.

Key features: • Many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory • A large number of exercises at various levels of difficulty • Some Euclidean geometry is included along with the theory of convex polyhedra • Few prerequisites are necessary beyond linear algebra and the basic notions of group theory.

The exposition is directed at advanced undergraduates and first-year graduate students.

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This is an incomplete draft version from 2000, not the published book.

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