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Abstract Regular Polytopes (Encyclopedia of Mathematics and its Applications) Hardcover – 12 Dec 2002

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'The book gives a comprehensive, complete overview of recent developments in a n important area of discrete geometry. it really fills an existing gap … and it shows in an impressive manner the interplay between the different methods that are important in this field. It can be strongly recommended to researchers and graduate students working in geometry, combinatorics and group theory.' Bulletin of the London Mathematical Society

'This book should be properly seen as the primary reference for the theory of abstract polytopes, especially of abstract regular polytopes … The book is very comprehensive and deep in its coverage of the topic. Almost everything known about abstract regular polytopes until the date of publication may be found somewhere within its 551 pages.' Zentralblatt MATH

Book Description

Abstract regular polytopes are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties. This comprehensive up-to-date account of the subject meets a critical need for a text in this area; no book has been published in this topic since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974).

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Necessary But Not Sufficient Reference Text 26 Nov. 2014
By David Harlco - Published on
Format: Hardcover
This book is a must-have for anyone serious about research in the field of abstract polytopes. The main thread of the book follows, as might be expected, the main thread of the authors' research up until the date of the book's publication. For this reason, it may underemphasise the work of other researchers in the field - although, at the time of the book's publication at least, McMullen and Schulte were indeed the leading researchers, so the view of the field is not too imbalanced.

Note that since the book's publication, there have been huge advances in the field of abstract polytopes. Don't expect a book from 2003 to be up-to-date for 2015!
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