Polytopes and Symmetry

Erscheinungsjahr 1984
ISBN: 978-0-521-27739-6
Verlag: Cambridge University Press

Buch, Englisch, Band 90, 128 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 203 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Robertson, Stewart A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.