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On m-point homogeneous polytopes in Euclidean spaces Full article

Journal Filomat
ISSN: 0354-5180
Output data Year: 2023, Volume: 37, Number: 25, Pages: 8405-8424 Pages count : 20 DOI: 10.2298/FIL2325405B
Tags Archimedean solid; Finite homogeneous metric space; Gosset polytope; m-point homogeneous metric space; Platonic solid; Point homogeneity degree; Regular polytope; Semiregular polytope
Authors Berestovskii Valeri˘ı Nikolaevich 1 , Nikonorov Yuri˘ı Gennadievich 2
Affiliations
1 Sobolev Inst Math SB RAS, 4 Acad,Koptyug Ave, Novosibirsk 630090, Russia
2 Vladikavkaz Scientific Center Southern Mathematical Institute VSC RAS

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0006

Abstract: This paper is devoted to the study the m-point homogeneity property and the point homo-geneity degree for finite metric spaces. Since the vertex sets of regular polytopes, as well as of some their generalizations, are homogeneous, we pay much attention to the study of the homogeneity properties of the vertex sets of polytopes in Euclidean spaces. Among main results, there is a classification of polyhedra with all edges of equal length and with 2-point homogeneous vertex sets. In addition, a significant part of the paper is devoted to the development of methods and tools for studying the relevant objects.
Cite: Berestovskii V.N. , Nikonorov Y.G.
On m-point homogeneous polytopes in Euclidean spaces
Filomat. 2023. V.37. N25. P.8405-8424. DOI: 10.2298/FIL2325405B WOS Scopus РИНЦ OpenAlex
Dates:
Submitted: Jul 8, 2022
Accepted: Dec 22, 2022
Published print: Aug 7, 2023
Published online: Aug 7, 2023
Identifiers:
Web of science: WOS:001024371100001
Scopus: 2-s2.0-85159633466
Elibrary: 67670304
OpenAlex: W4283713914
Citing:
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Scopus 2
OpenAlex 1
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