The Semiregular Polytopes of the Hyperspaces PDF Download
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Author: Emanuel Lodewijk Elte
Publisher:
ISBN:
Category : Hyperspace
Languages : en
Pages : 145
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Book Description
Author: Emanuel Lodewijk Elte
Publisher:
ISBN:
Category : Hyperspace
Languages : en
Pages : 145
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Book Description
Author: Tibor Bisztriczky
Publisher: Springer Science & Business Media
ISBN: 9401109249
Category : Mathematics
Languages : en
Pages : 515
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Book Description
The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.
Author: H. S. M. Coxeter
Publisher: Courier Corporation
ISBN: 0486141586
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.
Author: Peter McMullen
Publisher: Cambridge University Press
ISBN: 1108788319
Category : Mathematics
Languages : en
Pages : 617
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Book Description
Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.
Author: Koninklijke Nederlandse Akademie van Wetenschappen. Afdeling Natuurkunde
Publisher:
ISBN:
Category : Natural history
Languages : en
Pages : 1408
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Book Description
Author: Peter McMullen
Publisher: Cambridge University Press
ISBN: 9780521814966
Category : Mathematics
Languages : en
Pages : 580
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Book 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.
Author: H. S. M. Coxeter
Publisher: Courier Corporation
ISBN: 0486409198
Category : Mathematics
Languages : en
Pages : 301
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Book Description
Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 132
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Book Description
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 876
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Book Description
Author: GRUBER
Publisher: Birkhäuser
ISBN: 3034858582
Category : Science
Languages : en
Pages : 419
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Book Description
This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.
