Author: Laith RastanawiPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
On 4-Dimensional Point Groups and on Realization Spaces of Polytopes
Author: Laith RastanawiRealization Spaces of Polytopes
Author: Jürgen Richter-GebertPublisher: Springer
ISBN: 3540496408
Category : Mathematics
Languages : en
Pages : 195
Book Description
The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.
The Geometry of Higher-Dimensional Polytopes
Author: Zhizhin, Gennadiy VladimirovichPublisher: IGI Global
ISBN: 1522569693
Category : Technology & Engineering
Languages : en
Pages : 301
Book Description
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.
Realization Spaces of 4-polytopes are Universal
Author: J. Richter-GebertRealization spaces of 4-polytopes are universal
Author: Jürgen Richter-GebertPublisher:
ISBN:
Category :
Languages : de
Pages : 111
Book Description
Geometric Regular Polytopes
Author: Peter McMullenPublisher: Cambridge University Press
ISBN: 1108788319
Category : Mathematics
Languages : en
Pages : 617
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.
The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
Author: Zhizhin, Gennadiy VladimirovichPublisher: IGI Global
ISBN: 1799883760
Category : Mathematics
Languages : en
Pages : 366
Book Description
The study of the geometry of structures that arise in a variety of specific natural systems, such as chemical, physical, biological, and geological, revealed the existence of a wide range of types of polytopes of the highest dimension that were unknown in classical geometry. At the same time, new properties of polytopes were discovered as well as the geometric patterns to which they obey. There is a need to classify these types of polytopes of the highest dimension by listing their properties and formulating the laws to which they obey. The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems explains the meaning of higher dimensions and systematically generalizes the results of geometric research in various fields of knowledge. This book is useful both for the fundamental development of geometry and for the development of branches of science related to human activities. It builds upon previous books published by the author on this topic. Covering areas such as heredity, geometry, and dimensions, this reference work is ideal for researchers, scholars, academicians, practitioners, industry professionals, instructors, and students.
Regular Polytopes
Author: Harold Scott Macdonald CoxeterPublisher: Courier Corporation
ISBN: 9780486614809
Category : Mathematics
Languages : en
Pages : 372
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.
Polytopes and Symmetry
Author: Stewart A. RobertsonPublisher: Cambridge University Press
ISBN: 9780521277396
Category : Mathematics
Languages : en
Pages : 138
Book Description
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.
Abstract Regular Polytopes
Author: Peter McMullenPublisher: Cambridge University Press
ISBN: 9780521814966
Category : Mathematics
Languages : en
Pages : 580
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.