Abstract Regular Polytopes
Series: Encyclopedia of Mathematics and its Applications; 92;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 12 December 2002
- ISBN 9780521814966
- Binding Hardback
- No. of pages566 pages
- Size 241x164x33 mm
- Weight 970 g
- Language English
- Illustrations 65 b/w illus. 23 tables 0
Categories
Short description:
A modern, comprehensive review of abstract regular polytopes.
MoreLong description:
Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book should be of interest to researchers and graduate students in discrete geometry, combinatorics and group theory.
'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
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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