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Regular Complex Polytopes

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Regular Complex Polytopes

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Author : H. S. M. Coxeter
language : en
Publisher: Cambridge University Press
Release Date : 1991-04-26

Regular Complex Polytopes written by H. S. M. Coxeter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-26 with Mathematics categories.

The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra.

Regular Complex Polytopes

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Author : Coxeter
language : en
Publisher: Cambridge University Press
Release Date : 1975-03-06

Regular Complex Polytopes written by Coxeter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-03-06 with Mathematics categories.

Regular Complex Polytopes

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Author : Coxeter
language : en
Publisher: Cambridge University Press
Release Date : 1975-03-06

Abstract Regular Polytopes

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Author : Peter McMullen
language : en
Publisher: Cambridge University Press
Release Date : 2002-12-12

Abstract Regular Polytopes written by Peter McMullen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-12 with Mathematics categories.

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.

Regular Complex Polytopes Coxeter

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Author : Harold Scott Macdonald Coxeter
language : en
Publisher:
Release Date : 1974

Regular Complex Polytopes Coxeter written by Harold Scott Macdonald Coxeter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.

Regular Polytopes

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Author : Harold Scott Macdonald Coxeter
language : en
Publisher: Courier Corporation
Release Date : 1973-01-01

Regular Polytopes written by Harold Scott Macdonald Coxeter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-01-01 with Mathematics categories.

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.

Regular Polytopes

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Author : H. S. M. Coxeter
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23

Regular Polytopes written by H. S. M. Coxeter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.

Grobner Bases And Convex Polytopes

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Author : Bernd Sturmfels
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Grobner Bases And Convex Polytopes written by Bernd Sturmfels and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.

Lectures On Polytopes

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Author : Günter M. Ziegler
language : en
Publisher: Springer
Release Date : 2012-05-03

Lectures On Polytopes written by Günter M. Ziegler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-03 with Mathematics categories.

Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

Polytopes And Symmetry

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Author : Stewart A. Robertson
language : en
Publisher: Cambridge University Press
Release Date : 1984-01-26

Polytopes And Symmetry written by Stewart A. Robertson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-26 with Mathematics categories.

This book describes a fresh approach to the classification of of convex plane polygons and of convex polyhedra according to their symmetry properties, based on ideas of topology and transformation group theory. Although there is considerable agreement with traditional treatments, a number of new concepts emerge that present classical ideas in a quite new way.

Regular Complex Polytopes

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