Geometric Regular Polytopes

Inbunden, Engelska, 2020

Del 172 i serien Encyclopedia of Mathematics and its Applications

1 732 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:2020-02-20
Mått:160 x 240 x 32 mm
Vikt:1 100 g
Format:Inbunden
Språk:Engelska
Serie:Encyclopedia of Mathematics and its Applications
Antal sidor:619
Förlag:Cambridge University Press
ISBN:9781108489584

Utforska kategorier

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.