Mirrors and Reflections

Authors:

ISBN: 978-0-387-79065-7 (Print) 978-0-387-79066-4 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xii

  2. Geometric Background

    1. No Access

      Book Chapter

      Pages 3-10

      Affine Euclidean Space \(\mathbb{A}\mathbb{R}^{n}\)

    2. No Access

      Book Chapter

      Pages 11-16

      Isometries of \(\mathbb{A}\mathbb{R}^{n}\)

    3. No Access

      Book Chapter

      Pages 17-23

      Hyperplane Arrangements

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      Book Chapter

      Pages 25-34

      Polyhedral Cones

  3. Mirrors, Reflections, Roots

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      Book Chapter

      Pages 37-40

      Mirrors and Reflections

    2. No Access

      Book Chapter

      Pages 41-47

      Systems of Mirrors

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      Book Chapter

      Pages 49-53

      Dihedral Groups

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      Book Chapter

      Pages 55-62

      Root Systems

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      Book Chapter

      Pages 63-75

      Root Systems A nāˆ’1, BC n , D n

  4. Coxeter Complexes

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      Book Chapter

      Pages 79-82

      Chambers

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      Book Chapter

      Pages 83-90

      Generation

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      Book Chapter

      Pages 91-97

      Coxeter Complex

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      Book Chapter

      Pages 99-104

      Residues

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      Book Chapter

      Pages 105-109

      Generalized Permutahedra

  5. Classification

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      Book Chapter

      Pages 113-116

      Generators and Relations

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      Book Chapter

      Pages 117-122

      Classification of Finite Reflection Groups

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      Book Chapter

      Pages 123-131

      Construction of Root Systems

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      Book Chapter

      Pages 133-135

      Orders of Reflection Groups

  6. Three-Dimensional Reflection Groups

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      Book Chapter

      Pages 139-146

      Reflection Groups in Three Dimensions

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      Book Chapter

      Pages 147-153

      Icosahedron

  7. Back Matter

    Pages 155-171