Abstract Regular Polytopes

Peter McMullen, Egon Schulte

564 pages, parution le 31/12/2002

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Résumé

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.

Contents

Classical Regular Polytopes
Regular Polytopes
Coxeter Groups
Amalgamation
Realizations
Regular Polytopes on Space-Forms
Mixing
Twisting
Unitary Groups and Hermitian Forms
Locally Toroidal 4-Polytopes: I
Locally Toroidal 4-Polytopes: II
Higher Toroidal Polytopes
Regular Polytopes Related to Linear Groups
Miscellaneous Classes of Regular Polytopes

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Peter McMullen, Egon Schulte
Parution	31/12/2002
Nb. de pages	564
Format	16,2 x 24,2
Couverture	Relié
Poids	957g
Intérieur	Noir et Blanc
EAN13	9780521814966
ISBN13	978-0-521-81496-6