{"title":"论 3 美元欧几里得三维空间中的 m 美元点均质多面体","authors":"V. N. Berestovskii, Yu. G. Nikonorov","doi":"arxiv-2408.09911","DOIUrl":null,"url":null,"abstract":"This paper is devoted to the study of the $m$-point homogeneity property for\nthe vertex sets of polytopes in Euclidean spaces. In particular, we present the\nclassifications of $2$-point and $3$-point homogeneous polyhedra in\n$\\mathbb{R}^3$.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":"160 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space\",\"authors\":\"V. N. Berestovskii, Yu. G. Nikonorov\",\"doi\":\"arxiv-2408.09911\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to the study of the $m$-point homogeneity property for\\nthe vertex sets of polytopes in Euclidean spaces. In particular, we present the\\nclassifications of $2$-point and $3$-point homogeneous polyhedra in\\n$\\\\mathbb{R}^3$.\",\"PeriodicalId\":501444,\"journal\":{\"name\":\"arXiv - MATH - Metric Geometry\",\"volume\":\"160 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Metric Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.09911\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.09911","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space
This paper is devoted to the study of the $m$-point homogeneity property for
the vertex sets of polytopes in Euclidean spaces. In particular, we present the
classifications of $2$-point and $3$-point homogeneous polyhedra in
$\mathbb{R}^3$.