О Сложности Выпуклых Стереоэдров

Тарасов, Алексей Сергеевич; Tarasov, Aleksey Srgeevich

doi:10.4213/mzm1563

Mat. Zametki

1997

DOI: 10.4213/mzm1563

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О Сложности Выпуклых Стереоэдров

Алексей Сергеевич Тарасов¹,

Aleksey Srgeevich Tarasov²

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2021

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Nanostructures as Tillings of Higher Dimension Spaces

2021

Nanotechnologies and Clusters in the Spaces of Higher Dimension

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It is proved that clusters in the form of the 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 construction of n-dimensional spaces from congruent figures. Moreover, they create extended nanomaterials, in principle, of any size. General principles and an analytical method for constructing n-dimensional spaces with the help of polytopic prismahedrons are developed. On the example of specific types of the polytopic prismahedrons (tetrahedral prism, triangular prismahedron), the possibility of such constructions is analytically proved. It was found that neighboring polytopic prismahedrons in these constructions can have common geometric elements of any dimension less than n or do not have common elements.

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Nanostructures as Tillings of Higher Dimension Spaces

2021

Nanotechnologies and Clusters in the Spaces of Higher Dimension

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show abstract

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О Сложности Выпуклых Стереоэдров

Cited by 1 publication

References 4 publications

Nanostructures as Tillings of Higher Dimension Spaces

Nanostructures as Tillings of Higher Dimension Spaces

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