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On the Structure of Parallelohedrons of Higher Dimension: Hilbert's 18th Problem

On the Structure of Parallelohedrons of Higher Dimension: Hilbert's 18th Problem

Gennadiy Vladimirovich Zhizhin
Copyright: © 2019 |Volume: 8 |Issue: 2 |Pages: 28
ISSN: 2155-4110|EISSN: 2155-4129|EISBN13: 9781522567097|DOI: 10.4018/IJCCE.20190701.oa2
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MLA

Zhizhin, Gennadiy Vladimirovich. "On the Structure of Parallelohedrons of Higher Dimension: Hilbert's 18th Problem." IJCCE vol.8, no.2 2019: pp.69-96. http://doi.org/10.4018/IJCCE.20190701.oa2

APA

Zhizhin, G. V. (2019). On the Structure of Parallelohedrons of Higher Dimension: Hilbert's 18th Problem. International Journal of Chemoinformatics and Chemical Engineering (IJCCE), 8(2), 69-96. http://doi.org/10.4018/IJCCE.20190701.oa2

Chicago

Zhizhin, Gennadiy Vladimirovich. "On the Structure of Parallelohedrons of Higher Dimension: Hilbert's 18th Problem," International Journal of Chemoinformatics and Chemical Engineering (IJCCE) 8, no.2: 69-96. http://doi.org/10.4018/IJCCE.20190701.oa2

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Abstract

For more than 100 years in science, many researchers, when trying to solve Hilbert's 18th problem of constructing n-dimensional space, used the principles of the Delaunay geometric theory. In this paper, as a result of a careful analysis of the work in this direction, it is shown that the principles of the Delaunay theory are erroneous. They do not take into account the features of figures of higher dimensionality, do not agree with modern advances in the physics of the structure of matter, and lead to erroneous results. A new approach to solving the 18th Hilbert problem, based on modern knowledge in the field of the structure of matter and the geometric properties of figures of higher dimension, is proposed. The basis of the new approach to solving the 18th Hilbert problem is the theory developed by the author on polytopic prismahedrons.