论文标题
在$ m $ - 点均匀的欧几里得空间中
On $m$-point homogeneous polytopes in Euclidean spaces
论文作者
论文摘要
本文致力于研究$ m $ - 点同质性属性和有限度量空间的点同质性学位。由于正规多型的顶点集以及它们的某些概括是均匀的，因此我们非常关注欧几里得空间中多型顶点的均匀性属性的研究。在主要结果中，有一个分类的多面体，所有边缘的长度相等，并且具有2分均匀的顶点集。此外，本文的很大一部分致力于开发研究相关对象的方法和工具。
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.
