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ON FINITE HOMOGENEOUS METRIC SPACES# [О КОНЕЧНЫХ ОДНОРОДНЫХ МЕТРИЧЕСКИХ ПРОСТРАНСТВАХ] Full article

Journal Владикавказский математический журнал (Vladikavkaz Mathematical Journal)
ISSN: 1814-0807
Output data Year: 2022, Volume: 24, Number: 2, Pages: 51-61 Pages count : 11 DOI: 10.46698/h7670-4977-9928-z
Tags Archimedean solid; finite Clifford — Wolf homogeneous metric space; finite homogeneous metric space; finite normal homogeneous metric space; Gosset polytope; Platonic solid; regular polytope; semiregular polytope
Authors Berestovskiı V.N. 1 , Nikonorov Yu.G. 2
Affiliations
1 Sobolev Institute of Mathematics SB RAS, 4 Acad. Koptyug Ave., Novosibirsk, 630090, Russian Federation
2 Southern Mathematical Institute VSC RAS, 53 Vatutina St., Vladikavkaz, 362025, Russian Federation

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0006

Abstract: This survey is devoted to recently obtained results on finite homogeneous metric spaces. The main subject of discussion is the classification of regular and semiregular polytopes in Euclidean spaces by whether or not their vertex sets have the normal homogeneity property or the Clifford — Wolf homogeneity property. Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces. The normal generalized homogeneity and the Clifford — Wolf homogeneity describe more stronger properties than the homogeneity. Therefore, it is natural to first check the presence of these properties for the vertex sets of regular and semiregular polytopes. In addition to the classification results, the paper contains a description of the main tools for the study of the relevant objects. © 2022 Teoria ta Metodika Fizicnogo Vihovanna. All rights reserved.
Cite: Berestovskiı V.N. , Nikonorov Y.G.
ON FINITE HOMOGENEOUS METRIC SPACES# [О КОНЕЧНЫХ ОДНОРОДНЫХ МЕТРИЧЕСКИХ ПРОСТРАНСТВАХ]
Владикавказский математический журнал (Vladikavkaz Mathematical Journal). 2022. V.24. N2. P.51-61. DOI: 10.46698/h7670-4977-9928-z Scopus РИНЦ OpenAlex
Identifiers:
Scopus: 2-s2.0-85133733795
Elibrary: 49023147
OpenAlex: W4283393649
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