Compound Polytopes

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The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems

Author : Zhizhin, Gennadiy Vladimirovich
Publisher : IGI Global
ISBN 13 : 1799883760
Total Pages : 366 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems by : Zhizhin, Gennadiy Vladimirovich

Download or read book The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2022-04-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chemical Compound Structures and the Higher Dimension of Molecules: Emerging Research and Opportunities

Author : Zhizhin, Gennadiy Vladimirovich
Publisher : IGI Global
ISBN 13 : 1522541098
Total Pages : 235 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis Chemical Compound Structures and the Higher Dimension of Molecules: Emerging Research and Opportunities by : Zhizhin, Gennadiy Vladimirovich

Download or read book Chemical Compound Structures and the Higher Dimension of Molecules: Emerging Research and Opportunities written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2017-12-08 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally, scientists believed that molecules were three-dimensional; however, studies have proven that geometric dimensions are continuous. Therefore, molecules are able to have higher dimensions which influences how they interact with other molecules leading to advances in various fields including nanomedicine, nanotoxicology and quantum biology. Chemical Compound Structures and the Higher Dimension of Molecules: Emerging Research and Opportunities is a pivotal reference work studying the relationship between chemical compounds and dimensional space. Featuring comprehensive coverage across a range of related topics, such as convex polytypes, Euler-Poincaré equations, intermolecular interactions, and the Schrodiner equation, this book is an ideal reference source for academicians, researchers, and advance-level students seeking innovative research on molecule dimensions and interactions.

Regular Polytopes

Author : H. S. M. Coxeter
Publisher : Courier Corporation
ISBN 13 : 0486141586
Total Pages : 372 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Regular Polytopes by : H. S. M. Coxeter

Download or read book Regular Polytopes written by H. S. M. Coxeter and published by Courier Corporation. This book was released on 2012-05-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Polyhedron Models

Author : Magnus J. Wenninger
Publisher : Cambridge University Press
ISBN 13 : 9780521098595
Total Pages : 224 pages
Book Rating : 4.0/5 (985 download)

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Book Synopsis Polyhedron Models by : Magnus J. Wenninger

Download or read book Polyhedron Models written by Magnus J. Wenninger and published by Cambridge University Press. This book was released on 1971 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: he author describes simply and carefully how to make models of all the known uniform polyhedra and some of the stellated forms.

Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces

Author : Zhizhin, Gennadiy Vladimirovich
Publisher : IGI Global
ISBN 13 : 1799867706
Total Pages : 280 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces by : Zhizhin, Gennadiy Vladimirovich

Download or read book Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2020-12-25 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of the structure of substances in recent decades, phenomena in the higher dimension was discovered that was previously unknown. These include spontaneous zooming (scaling processes), discovery of crystals with the absence of translational symmetry in three-dimensional space, detection of the fractal nature of matter, hierarchical filling of space with polytopes of higher dimension, and the highest dimension of most molecules of chemical compounds. This forces research to expand the formulation of the question of constructing n-dimensional spaces, posed by David Hilbert in 1900, and to abandon the methods of considering the construction of spaces by geometric figures that do not take into account the accumulated discoveries in the physics of the structure of substances. There is a need for research that accounts for the new paradigm of the discrete world and provides a solution to Hilbert's 18th problem of constructing spaces of higher dimension using congruent figures. Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces aims to consider the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space. This book considers the conditions of existence of polytopes of higher dimension, clusters of chemical compounds as polytopes of the highest dimension, higher dimensions in the theory of heredity, the geometric structure of the product of polytopes, the products of polytopes on clusters and molecules, parallelohedron and stereohedron of Delaunay, parallelohedron of higher dimension and partition of n-dimensional spaces, hierarchical filling of n-dimensional spaces, joint normal partitions, and hierarchical fillings of n-dimensional spaces. In addition, it pays considerable attention to biological problems. This book is a valuable reference tool for practitioners, stakeholders, researchers, academicians, and students who are interested in learning more about the latest research on normal partitions and hierarchical fillings of n-dimensional spaces.

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory

Author : Gareth A. Jones
Publisher : Springer Nature
ISBN 13 : 3030328082
Total Pages : 239 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Isomorphisms, Symmetry and Computations in Algebraic Graph Theory by : Gareth A. Jones

Download or read book Isomorphisms, Symmetry and Computations in Algebraic Graph Theory written by Gareth A. Jones and published by Springer Nature. This book was released on 2020-01-10 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Complex Symmetries

Author : György Darvas
Publisher : Springer Nature
ISBN 13 : 3030880591
Total Pages : 262 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Complex Symmetries by : György Darvas

Download or read book Complex Symmetries written by György Darvas and published by Springer Nature. This book was released on 2022-01-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries). These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.

Convexity from the Geometric Point of View

Author : Vitor Balestro
Publisher : Springer Nature
ISBN 13 : 3031505077
Total Pages : 1195 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Convexity from the Geometric Point of View by : Vitor Balestro

Download or read book Convexity from the Geometric Point of View written by Vitor Balestro and published by Springer Nature. This book was released on with total page 1195 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Kaleidoscopes

Author : F. Arthur Sherk
Publisher : John Wiley & Sons
ISBN 13 : 9780471010036
Total Pages : 476 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Kaleidoscopes by : F. Arthur Sherk

Download or read book Kaleidoscopes written by F. Arthur Sherk and published by John Wiley & Sons. This book was released on 1995-05-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: H.S.M. Coxeter is one of the world's best-known mathematicians who wrote several papers and books on geometry, algebra and topology, and finite mathematics. This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

The Geometry of Higher-Dimensional Polytopes

Author : Zhizhin, Gennadiy Vladimirovich
Publisher : IGI Global
ISBN 13 : 1522569693
Total Pages : 301 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis The Geometry of Higher-Dimensional Polytopes by : Zhizhin, Gennadiy Vladimirovich

Download or read book The Geometry of Higher-Dimensional Polytopes written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2018-08-03 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Geometry

Author : Andras Bezdek
Publisher : CRC Press
ISBN 13 : 0824747615
Total Pages : 500 pages
Book Rating : 4.8/5 (247 download)

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Book Synopsis Discrete Geometry by : Andras Bezdek

Download or read book Discrete Geometry written by Andras Bezdek and published by CRC Press. This book was released on 2003-02-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.

Regular Polytopes

Author : Harold Scott Macdonald Coxeter
Publisher :
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Regular Polytopes by : Harold Scott Macdonald Coxeter

Download or read book Regular Polytopes written by Harold Scott Macdonald Coxeter and published by . This book was released on 1948 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Regular Polytopes

Author : Peter McMullen
Publisher : Cambridge University Press
ISBN 13 : 1108788319
Total Pages : 617 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Geometric Regular Polytopes by : Peter McMullen

Download or read book Geometric Regular Polytopes written by Peter McMullen and published by Cambridge University Press. This book was released on 2020-02-20 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends in Intuitive Geometry

Author : Gergely Ambrus
Publisher : Springer
ISBN 13 : 3662574136
Total Pages : 461 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis New Trends in Intuitive Geometry by : Gergely Ambrus

Download or read book New Trends in Intuitive Geometry written by Gergely Ambrus and published by Springer. This book was released on 2018-11-03 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

The Geometric Vein

Author : C. Davis
Publisher : Springer Science & Business Media
ISBN 13 : 1461256488
Total Pages : 590 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Geometric Vein by : C. Davis

Download or read book The Geometric Vein written by C. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry has been defined as that part of mathematics which makes appeal to the sense of sight; but this definition is thrown in doubt by the existence of great geometers who were blind or nearly so, such as Leonhard Euler. Sometimes it seems that geometric methods in analysis, so-called, consist in having recourse to notions outside those apparently relevant, so that geometry must be the joining of unlike strands; but then what shall we say of the importance of axiomatic programmes in geometry, where reference to notions outside a restricted reper tory is banned? Whatever its definition, geometry clearly has been more than the sum of its results, more than the consequences of some few axiom sets. It has been a major current in mathematics, with a distinctive approach and a distinc ti v e spirit. A current, furthermore, which has not been constant. In the 1930s, after a period of pervasive prominence, it appeared to be in decline, even passe. These same years were those in which H. S. M. Coxeter was beginning his scientific work. Undeterred by the unfashionability of geometry, Coxeter pursued it with devotion and inspiration. By the 1950s he appeared to the broader mathematical world as a consummate practitioner of a peculiar, out-of-the-way art. Today there is no longer anything that out-of-the-way about it. Coxeter has contributed to, exemplified, we could almost say presided over an unanticipated and dra matic revival of geometry.

The Coxeter Legacy

Author : Harold Scott Macdonald Coxeter
Publisher : American Mathematical Soc.
ISBN 13 : 9780821887608
Total Pages : 344 pages
Book Rating : 4.8/5 (876 download)

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Book Synopsis The Coxeter Legacy by : Harold Scott Macdonald Coxeter

Download or read book The Coxeter Legacy written by Harold Scott Macdonald Coxeter and published by American Mathematical Soc.. This book was released on with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.

Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn

Author : Michel-marie Deza
Publisher : World Scientific
ISBN 13 : 1783260866
Total Pages : 186 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn by : Michel-marie Deza

Download or read book Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn written by Michel-marie Deza and published by World Scientific. This book was released on 2004-02-13 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph identifies polytopes that are “combinatorially ℓ1-embeddable”, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to “ℓ2-prominent” affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability — the main unifying question, to which those lists are subjected — is presented with the minimum of technicalities.