Geometric Regular Polytopes

The first comprehensive account of modern geometric theory and its applications, written by a leader in the field.

Peter McMullen (Author)

9781108489584, Cambridge University Press

Hardback, published 20 February 2020

619 pages, 43 b/w illus. 19 colour illus. 3 tables
24 x 16 x 3.2 cm, 1.1 kg

'The book is without a doubt a modern bible on the current state of polytopes. It is no exaggeration to say that 'all of it' can be found in this book …' Peter McMullen, Nieuw Archief voor Wiskunde

Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.

Foreword
Part I. Regular Polytopes: 1. Euclidean space
2. Abstract regular polytopes
3. Realizations of symmetric sets
4. Realizations of polytopes
5. Operations and constructions
6. Rigidity
Part II. Polytopes of Full Rank: 7. Classical regular polytopes
8. Non-classical polytopes
Part III. Polytopes of Nearly Full Rank: 9. General families
10. Three-dimensional apeirohedra
11. Four-dimensional polyhedra
12. Four-dimensional apeirotopes
13. Higher-dimensional cases
Part IV. Miscellaneous Polytopes: 14. Gosset–Elte polytopes
15. Locally toroidal polytopes
16. A family of 4-polytopes
17. Two families of 5-polytopes
Afterword
References
Symbol index
Author index
Subject index.

Subject Areas: Geometry [PBM], Discrete mathematics [PBD]