Geometric Regular Polytopes
Geometric Regular Polytopes
£117.00
GBPRegular 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.
- Provides the first comprehensive coverage of the modern geometric theory
- Uses an elementary approach to topics and collects basic theory in one place, making it suitable for graduate students
- Introduces new techniques for the use of researchers
Reviews & endorsements
'McMullen (emer., University College London) begins the text with a rapid, cogent review of relevant topics in linear algebra and group theory and proceeds to a thorough discussion of the properties and structures of geometric and abstract regular polytopes. The majority of the text details the classification and properties of geometric regular polytopes … This is a careful, comprehensive survey of the topic and will likely become a classic reference.' C. A. Gorini, Choice
'This book, along with his previous book … is well-written and indispensable for every researcher or every student who wants to pursue research in this area.' Uma Kant Sahoo, Encyclopedia of Mathematics and its Applications
'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
'Whether you are an experienced researcher in the subject, a mathematician seeking to expand their research interests to include this subject area, or a student beginning their polytopal journey, this book is a great source of knowledge on the geometric perspective of regular polytopes.' Andrés R. Vindas-Meléndez, MathSciNet
Product details
February 2020Hardback
9781108489584
619 pages
240 × 160 × 32 mm
1.1kg
43 b/w illus. 19 colour illus. 3 tables
Available
Table of Contents
- 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.
