'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
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).