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Polytopes and Symmetry

Polytopes and Symmetry

£27.99

Part of London Mathematical Society Lecture Note Series

  • Date Published: January 1984
  • availability: Available
  • format: Paperback
  • isbn: 9780521277396

£ 27.99
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  • Convex polytopes are the analogues in space of any dimension of convex plane polygons and of convex polyhedra in ordinary space. This book describes a fresh approach to the classification of these objects according to their symmetry properties, based on ideas of topology and transformation group theory. Although there is considerable agreement with traditional treatments, a number of new concepts emerge that present classical ideas in a quite new way. For example, the family of regular convex polytopes is extended to the family of 'perfect polytopes'. Thus the familiar set of five Platonic polyhedra is replaced by the less familiar set of nine perfect polyhedra. Among the many unsolved problems that arise, that of finding all perfect polytopes, and more generally all perfect convex bodies, is perhaps the most attractive. This book will be of value to specialists and graduate students in pure mathematics, especially those studying symmetry theory, convex bodies, and polytopes.

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    Product details

    • Date Published: January 1984
    • format: Paperback
    • isbn: 9780521277396
    • length: 132 pages
    • dimensions: 229 x 153 x 17 mm
    • weight: 0.223kg
    • availability: Available
  • Table of Contents

    Preface
    Synopsis
    1. The space of polytopes
    2. Combinatorial structure
    3. Symmetry equivalence
    4. Products and sums
    5. Polygons
    6. Polyhedra
    Concluding remarks
    Bibliography
    Index of symbols
    Index of names
    General index.

  • Author

    Stewart A. Robertson

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