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What is Poly-Incident Polytopes

Chapter 5
Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
The product of icosahedron by the triangle.
Published in Chapter:
The Geometric Structure of the Product of Polytopes
Copyright: © 2021 |Pages: 33
DOI: 10.4018/978-1-7998-6768-5.ch005
Abstract
The structure of polytopes of higher dimension (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, their investigations are of independent interest. Analytical dependencies characterizing the structure of the product of polytopes are obtained as a function of the structures of polytope factors. Images of a number of specific polytopic prismahedrons are obtained, and tables of structures of polytopic prismahedrons are compiled depending on the types of polytopes of the factors. The geometric properties of the boundary complexes of polytopic prismahedrons are investigated.
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Chapter 5
The Geometric Structure of the Product of Polytopes
Full Text Chapter Download: US $37.50 Add to Cart
Chapter 9
Hierarchical Filling of N-Dimensional Spaces
A series of numbers in which a member of a series is the sum of the two previous members of the series.
Published in Chapter: Hierarchical Filling of N-Dimensional Spaces; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 5
The Geometric Structure of the Product of Polytopes
Full Text Chapter Download: US $37.50 Add to Cart
Chapter 5
The Geometric Structure of the Product of Polytopes
Full Text Chapter Download: US $37.50 Add to Cart
Chapter 5
The Geometric Structure of the Product of Polytopes
Full Text Chapter Download: US $37.50 Add to Cart
Chapter 5
The Geometric Structure of the Product of Polytopes
Full Text Chapter Download: US $37.50 Add to Cart
Chapter 8
Polytopes Dual to Higher-Dimensional Polytopes
Polytopes in which elements of lower dimension have different incidence values for elements of higher dimension. Polytopes that are dual to polytopes products are poly-incident polytopes.
Published in Chapter: Polytopes Dual to Higher-Dimensional Polytopes; From: The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems
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Chapter 5
The Geometric Structure of the Product of Polytopes
Full Text Chapter Download: US $37.50 Add to Cart
Chapter 7
Parallelohedrons and Stereohedrons of Delaunay
A polygon capable of filling a two-dimensional plane without gaps during its translation, with adjacent polygons adjacent to each other on the whole sides of the polygons.
Published in Chapter: Parallelohedrons and Stereohedrons of Delaunay; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 7
Parallelohedrons and Stereohedrons of Delaunay
A polyhedron capable of filling a three-dimensional space without gaps during its translation, with adjacent polyhedrons adjacent to each other along whole flat faces of the polyhedrons.
Published in Chapter: Parallelohedrons and Stereohedrons of Delaunay; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 5
The Geometric Structure of the Product of Polytopes
The product of 4-cross-polytope by one dimension segment.
Published in Chapter: The Geometric Structure of the Product of Polytopes; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 9
Hierarchical Filling of N-Dimensional Spaces
Filling a space with a figure with a similar increase in the size of the figure around a certain center according to some law related to the geometric characteristics of the figure itself.
Published in Chapter: Hierarchical Filling of N-Dimensional Spaces; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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Chapter 1
On the Conditions for the Existence of Higher-Dimensional Polytopes
Polytopes in which elements of lower dimension have different incidence values for elements of higher dimension. Polytopes that are dual to polytopes products are poly-incident polytopes.
Published in Chapter: On the Conditions for the Existence of Higher-Dimensional Polytopes; From: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces
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