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On $m$-point homogeneous polytopes in Euclidean spaces

Valerii N. BerestovskiiYurii G. Nikonorov
Jun 2022
摘要
This paper is devoted to the study the $m$-point homogeneity property and thepoint homogeneity degree for finite metric spaces. Since the vertex sets ofregular polytopes, as well as of some their generalizations, are homogeneous,we pay much attention to the study of the homogeneity properties of the vertexsets of polytopes in Euclidean spaces. Among main results, there is aclassification of polyhedra with all edges of equal length and with 2-pointhomogeneous vertex sets. In addition, a significant part of the paper isdevoted to the development of methods and tools for studying the relevantobjects.
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