ON FINITE HOMOGENEOUS METRIC SPACES# [О КОНЕЧНЫХ ОДНОРОДНЫХ МЕТРИЧЕСКИХ ПРОСТРАНСТВАХ] Full article
| Journal |
Владикавказский математический журнал (Vladikavkaz Mathematical Journal)
ISSN: 1814-0807 |
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| 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 | ||||
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| Affiliations |
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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
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 |