Articles liés à Convex Polytopes and Polyhedra

Convex Polytopes and Polyhedra - Couverture rigide

McMullen, Peter

 
9781009699983: Convex Polytopes and Polyhedra
Couverture rigide
ISBN 10 : 1009699989 ISBN 13 : 9781009699983
Editeur : Cambridge University Press, 2026

Synopsis

A valuable resource for researchers in discrete and combinatorial geometry, this book offers comprehensive coverage of several modern developments on algebraic and combinatorial properties of polytopes. The introductory chapters provide a new approach to the basic properties of convex polyhedra and how they are connected; for instance, fibre operations are treated early on. Finite tilings and polyhedral convex functions play an important role, and lead to the new technique of tiling diagrams. Special classes of polytopes such as zonotopes also have corresponding diagrams. A central result is the complete characterization of the possible face-numbers of simple polytopes. Tools used for this are representations and the weight algebra of mixed volumes. An unexpected consequence of the proof is an algebraic treatment of Brunn– Minkowski theory as applied to polytopes. Valuations also provide a thread running through the book, and the abstract theory and related tensor algebras are treated in detail.

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À propos de l'auteur

Peter McMullen is Professor Emeritus of Mathematics at University College London. He was elected a foreign member of the Austrian Academy of Sciences in 2006, and a fellow of the American Mathematical Society in 2012. He is also a member of the London and European Mathematical Societies. He has co-edited several books, has co-authored 'Abstract Regular Polytopes' (Cambridge, 2002) and written 'Geometric Regular Polytopes' (Cambridge, 2020). His work has been discussed in the 'Encyclopaedia Britannica', and he was an invited speaker at the International Congress of Mathematicians in 1974.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2026
Langue
anglais
ISBN 10 
1009699989
ISBN 13 
9781009699983
Reliure
Relié
Nombre de pages
654
Coordonnées du fabricant
Cambridge University Press
https://www.cambridge.org/

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