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Higher-Dimensional Space of Nanoworld

Higher-Dimensional Space of Nanoworld

Copyright: © 2021 |Pages: 30
ISBN13: 9781799837848|ISBN10: 179983784X|EISBN13: 9781799837855
DOI: 10.4018/978-1-7998-3784-8.ch001
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MLA

Gennadiy Vladimirovich Zhizhin. "Higher-Dimensional Space of Nanoworld." Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities, IGI Global, 2021, pp.1-30. https://doi.org/10.4018/978-1-7998-3784-8.ch001

APA

G. Zhizhin (2021). Higher-Dimensional Space of Nanoworld. IGI Global. https://doi.org/10.4018/978-1-7998-3784-8.ch001

Chicago

Gennadiy Vladimirovich Zhizhin. "Higher-Dimensional Space of Nanoworld." In Nanotechnologies and Clusters in the Spaces of Higher Dimension: Emerging Research and Opportunities. Hershey, PA: IGI Global, 2021. https://doi.org/10.4018/978-1-7998-3784-8.ch001

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Abstract

In this chapter, a geometrical model to accurately describe the distribution of light points in diffraction patterns of quasicrystals is proposed. It is shown that the proposed system of parallel lines has axes of the fifth order and periodically repeating the fundamental domain of the quasicrystals. This fundamental domain is 4D-polytope, called the golden hyper-rhombohedron. It consists of eight rhombohedrons densely filling the 4D space. Faces of the hyper-rhombohedron are connected by the golden section; they can be scaled as needed. On this universal lattice of the vertices of the golden hyper-rhombohedrons, famous crystallographic lattices—Bravais, Delone, Voronoi, etc.—can be embedded. On the lattice of the vertices of the golden hyper-rhombohedrons, projections of all regular three-dimensional convex bodies—Plato's bodies—can be constructed.

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