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What is Dimension of the Space

Chapter 1
The Geometry of Higher-Dimensional Polytopes
The number of independent parameters needed to describe the change in position of an object in space.
Published in Chapter:
Polytopes of Higher Dimension in the Nature
Copyright: © 2019 |Pages: 45
DOI: 10.4018/978-1-5225-6968-8.ch001
Abstract
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 properties of polytopes of higher dimension. This leads to the creation of higher-dimensional stereochemistry. Phase transitions of the second kind are accompanied by a change in the symmetry of the structure of matter, the description of which, in agreement with the experimental data, requires the attraction of spaces of higher dimension. Elementary cells of quasicrystals, having the form of polytopic prismahedrons, are given (polytopes of higher dimension). The structure of DNA as sequence of the higher dimensional polytopes are given.
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Chapter 2
Higher Dimensions of Clusters of Intermetallic Compounds
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Higher Dimensions of Clusters of Intermetallic Compounds; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 7
Three-Dimensional Models of a Five-Carbon Sugar Molecule and Nucleic Acids
The number of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Three-Dimensional Models of a Five-Carbon Sugar Molecule and Nucleic Acids; From: Attractors and Higher Dimensions in Population and Molecular Biology: Emerging Research and Opportunities
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Chapter 11
Polytopes of the Highest Dimension in the Theory of Heredity
The member of independent parameters needed to describe the change in position of an object in the space.
Published in Chapter: Polytopes of the Highest Dimension in the Theory of Heredity; From: The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
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Chapter 7
Incident Conservation Law
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Incident Conservation Law; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 5
Closed Metal Cycles in Clusters With Ligands
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Closed Metal Cycles in Clusters With Ligands; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 2
Clusters of Chemical Compounds as Polytopes of the Highest Dimension
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Clusters of Chemical Compounds as Polytopes of the Highest Dimension; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 8
The Geometry of the Structure of Nucleic Acids With Regard to the Higher Dimension of the Components
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Chapter 6
Metallic Clusters With Ligands and Polyhedral Core
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Metallic Clusters With Ligands and Polyhedral Core; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 7
Parallelohedrons and Stereohedrons of Delaunay
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Parallelohedrons and Stereohedrons of Delaunay; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 3
Necessary and Sufficient Conditions for Proving the Existence of Polytopes of Higher Dimension
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Necessary and Sufficient Conditions for Proving the Existence of Polytopes of Higher Dimension; From: The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
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Chapter 4
Higher Dimensions in the Theory of Heredity
The member of independent parameters needed to describe the change in position of an object in the space.
Published in Chapter: Higher Dimensions in the Theory of Heredity; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 1
Higher-Dimensional Space of Nanoworld
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Higher-Dimensional Space of Nanoworld; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 50
The Structure of DNA Taking Into Account the Higher Dimension of Its Components
The number of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: The Structure of DNA Taking Into Account the Higher Dimension of Its Components; From: Encyclopedia of Information Science and Technology, Fifth Edition
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Chapter 8
Parallelohedrons of Higher Dimension and Partition of N-Dimensional Spaces
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Parallelohedrons of Higher Dimension and Partition of N-Dimensional Spaces; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 4
Chains of Metallic Clusters With Ligands
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Chains of Metallic Clusters With Ligands; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 5
Irregular Polytopes of Higher Dimension
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Irregular Polytopes of Higher Dimension; From: The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
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Chapter 8
Mathematical Design of Nanomaterials From Clusters of Higher Dimension
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Mathematical Design of Nanomaterials From Clusters of Higher Dimension; From: Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities
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Chapter 4
Regular and Semi-Regular Polytopes of Higher Dimension
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: Regular and Semi-Regular Polytopes of Higher Dimension; From: The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
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Chapter 3
The Law of Conservation of Incidents in the Space of Nanoworld
The member of independent parameters needed to describe the change in position of an object in space.
Published in Chapter: The Law of Conservation of Incidents in the Space of Nanoworld; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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