Geodesic
On m-point homogeneous polytopes in Euclidean spaces
Filomat, Tome 37 (2023) no. 25, p. 8405

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DOI

This paper is devoted to the study the m-point homogeneity property and the point homogeneity 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.
DOI : 10.2298/FIL2325405B
Classification : 52B15, 54E35, 20B05
Keywords: Archimedean solid, Finite homogeneous metric space, Gosset polytope, m-point homogeneous metric space, Platonic solid, Point homogeneity degree, Regular polytope, Semiregular polytope 
Valeriĭ Nikolaevich Berestovskiĭ; Yuriĭ Gennadievich Nikonorov. On m-point homogeneous polytopes in Euclidean spaces. Filomat, Tome 37 (2023) no. 25, p. 8405 . doi: 10.2298/FIL2325405B
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     title = {On m-point homogeneous polytopes in {Euclidean} spaces},
     journal = {Filomat},
     pages = {8405 },
     year = {2023},
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     doi = {10.2298/FIL2325405B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325405B/}
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