{"title":"Properties of 3-Triangulations for p-Toroid","authors":"M. Stojanovic","doi":"10.30958/ajs.10-1-2","DOIUrl":null,"url":null,"abstract":"In this paper, a method for constructing a toroid and its decomposition into convex pieces is considered. A graph of connection for 3-triangulable toroid is introduced in such a way that these pieces are represented by graph nodes. It is shown that connected, nonorientable graph can serve as a graph of connection for some of the toroids. The relationship between graphs that can be realized on surfaces of different genus and corresponding toroids is considered. Keywords: 3-triangulation of polyhedra, toroids, piecewise convex polyhedra, graph of connection","PeriodicalId":91843,"journal":{"name":"Athens journal of sciences","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Athens journal of sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30958/ajs.10-1-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a method for constructing a toroid and its decomposition into convex pieces is considered. A graph of connection for 3-triangulable toroid is introduced in such a way that these pieces are represented by graph nodes. It is shown that connected, nonorientable graph can serve as a graph of connection for some of the toroids. The relationship between graphs that can be realized on surfaces of different genus and corresponding toroids is considered. Keywords: 3-triangulation of polyhedra, toroids, piecewise convex polyhedra, graph of connection
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