Table of Contents

Foreword; 1. Classical regular polytopes; 2. Regular polytopes; 3. Coxeter groups; 4. Amalgamation; 5. Realizations; 6. Regular polytopes on space-forms; 7. Mixing; 8. Twisting; 9. Unitary groups and hermitian forms; 10. Locally toroidal 4-polytopes: I; 11. Locally toroidal 4-polytopes: II; 12. Higher toroidal polytopes; 13. Regular polytopes related to linear groups; 14. Miscellaneous classes of regular polytopes; Bibliography; Indices.

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A modern, comprehensive review of abstract regular polytopes.

Reviews

'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