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Polytopes And Symmetry

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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.

Symmetries In Graphs Maps And Polytopes

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Author : Jozef Širáň
language : en
Publisher: Springer
Release Date : 2016-03-26

Symmetries In Graphs Maps And Polytopes written by Jozef Širáň and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-26 with Mathematics categories.

This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d’enfant.Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d’Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010.This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures.iv>

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.

Polytopes And Discrete Geometry

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Author : Gabriel Cunningham
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-06

Polytopes And Discrete Geometry written by Gabriel Cunningham 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 2021-04-06 with Education categories.

The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string C C-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas. Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string C C-groups; hypertopes; and graph coloring.

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.

Rigidity And Symmetry

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Author : Robert Connelly
language : en
Publisher: Springer
Release Date : 2014-06-11

Rigidity And Symmetry written by Robert Connelly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.

This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

The Geometry Of Higher Dimensional Polytopes

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Author : Zhizhin, Gennadiy Vladimirovich
language : en
Publisher: IGI Global
Release Date : 2018-08-03

The Geometry Of Higher Dimensional Polytopes written by Zhizhin, Gennadiy Vladimirovich and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-03 with Technology & Engineering categories.

The majority of the chemical elements form chemical compounds with molecules of higher dimension (i.e., substantially exceeding three). This fact is very important for the analysis of molecular interactions in various areas: nanomedicine, nanotoxicology, and quantum biology. The Geometry of Higher-Dimensional Polytopes contains innovative research on the methods and applications of the structures of binary compounds. It explores the study of geometry polytopes from a higher-dimensional perspective, taking into account the features of polytopes that are models of chemical compounds. While highlighting topics including chemical compounds, symmetry transformation, and DNA structures, this book is ideally designed for researchers, academicians, and students seeking current research on dimensions present in binary compounds.

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.

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.

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.

Geometric Combinatorics

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Author : Ezra Miller
language : en
Publisher: American Mathematical Soc.
Release Date :

Geometric Combinatorics written by Ezra Miller 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 with Mathematics categories.

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Polytopes And Symmetry

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