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The Geometry of Higher-Dimensional Polytopes

The Geometry of Higher-Dimensional Polytopes

Gennadiy Vladimirovich Zhizhin (Russian Academy of Sciences, Russia)
Copyright: © 2019 |Pages: 286
ISBN13: 9781522569688|ISBN10: 1522569685|ISBN13 Softcover: 9781522588221|EISBN13: 9781522569695
DOI: 10.4018/978-1-5225-6968-8
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MLA

Zhizhin, Gennadiy Vladimirovich. The Geometry of Higher-Dimensional Polytopes. IGI Global, 2019. http://doi:10.4018/978-1-5225-6968-8

APA

Zhizhin, G. V. (2019). The Geometry of Higher-Dimensional Polytopes. IGI Global. http://doi:10.4018/978-1-5225-6968-8

Chicago

Zhizhin, Gennadiy Vladimirovich. The Geometry of Higher-Dimensional Polytopes. Hershey, PA: IGI Global, 2019. http://doi:10.4018/978-1-5225-6968-8

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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.

Table of Contents

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Front Materials
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Title Page
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Copyright Page
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Advances in Chemical and Materials Engineering (ACME) Book Series
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Preface
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Chapters
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Chapter 1
Areas of research into the phenomena of nature in which the influence of polytopes of higher dimension is described in this chapter. These include studies of the structures of many chemical compounds whose molecules exhibit the...
Polytopes of Higher Dimension in the Nature
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Chapter 2
This chapter describes how the structure of a polytope of dimension n consisting of points of the boundary complex including a set of faces from zero to n - 1 and a set of interior points that are not belonging to the boundary...
Boundary Complexes and Interior Points of the Polytopes
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Chapter 3
The number of symmetry transformations of regular polytopes of dimension n (n - cubes, n - simplexes, n - cross polytopes) are considered, using symmetry transformation of their facets. In this chapter, it is investigated how a...
The Number of Symmetry Transformation of Convex Regular Polytopes in the n - Space
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Chapter 4
Polytopic Prismahedrons  (pages 103-144)
The structure of polytopes - polytopic prismahedrons, which are products of polytopes of lower dimensionality, is investigated. The products of polytopes do not belong to the well-studied class of simplicial polytopes, and therefore...
Polytopic Prismahedrons
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Chapter 5
The incidence of elements of low dimension in convex regular polytopes of dimension n with respect to elements of higher dimension up to elements of dimension n - 1 is investigated. It is shown that polytopes are dual to polytopic...
Poly - Incident and Dual Polytopes
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Chapter 6
The structure of the n – cross - polytopes for large values of n with an exact enumeration of elements of various dimensions entering their boundary complexes is studied in detail. Examples of chemical compounds with the structure of...
The Detailed Structure of n - Cross - Polytopes and Polytopes With Their Participation
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Chapter 7
The hierarchical filling of the n - dimensional space with geometric figures is studied, accompanied by a process of discrete similar changes in their dimensions, i.e. process of scaling. The scaling process in these fillings does...
Scaling in the Process of Hierarchical Filling of n - Dimensional Space
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Chapter 8
It is shown that the stationary Schrödinger equation describing the distribution of electrons in the vicinity of the atomic nucleus has a solution, in principle, for any dimensionality of the space around the nucleus. As an example...
On the Possible Electronic Structure of Atoms in a Space of Higher Dimension
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Chapter 9
It is proved that polytopic prismahedrons have the necessary properties for partitioning the n - dimensional spaces of a face into a face, that is, they satisfy the conditions for solving the eighteenth Hilbert problem of the...
The Partition of n – Dimensional Space of Polytopic Prismahedrons
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Back Materials
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Conclusion
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Index
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