Polytopes and Symmetry (London Mathematical Society Lecture Note Series, Series Number 90) (Volume 0) - Softcover

Robertson, Stewart A.

Softcover

ISBN 10: 0521277396 ISBN 13: 9780521277396

Publisher: Cambridge University Press, 1984

Synopsis

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.

About this title

Book Description

This book describes a fresh approach to the classification of of convex plane polygons and of convex polyhedra 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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1984
• Language: English
• ISBN 10: 0521277396
• ISBN 13: 9780521277396
• Binding: Paperback
• Edition number: 1
• Number of pages: 132