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.
Rezensionen / Stimmen
'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.' Andres R. Vindas-Melendez, MathSciNet
Reihe
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 3 Tables, black and white; 19 Line drawings, color; 43 Line drawings, black and white
Maße
Höhe: 325 mm
Breite: 241 mm
Dicke: 31 mm
Gewicht
ISBN-13
978-1-108-48958-4 (9781108489584)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Peter McMullen is Professor Emeritus of Mathematics at University College London. He was elected a foreign member of the Austrian Academy of Sciences in 2006 and is also a member of the London Mathematical Society and the European Mathematical Society. He was elected a Fellow of the American Mathematical Society in 2012. He has co-edited several books and co-authored Abstract Regular Polytopes (Cambridge, 2002). His work has been discussed in the Encyclopaedia Britannica and he was an invited speaker at the International Congress of Mathematicians in 1974.
Autor*in
University College London
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.
