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Geometric Regular Polytopes

Hardback

Main Details

Title Geometric Regular Polytopes
Authors and Contributors      By (author) Peter McMullen
SeriesEncyclopedia of Mathematics and its Applications
Physical Properties
Format:Hardback
Pages:619
Dimensions(mm): Height 240,Width 160
Category/GenreGeometry
ISBN/Barcode 9781108489584
ClassificationsDewey:516.158
Audience
Professional & Vocational
Postgraduate, Research & Scholarly
Illustrations Worked examples or Exercises; 3 Tables, black and white; 19 Line drawings, color; 43 Line drawings, black and white

Publishing Details

Publisher Cambridge University Press
Imprint Cambridge University Press
Publication Date 20 February 2020
Publication Country United Kingdom

Description

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.

Author Biography

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.

Reviews

'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