{"title":"p-环面最小三三角剖分","authors":"M. Stojanovic","doi":"10.2298/fil2301115s","DOIUrl":null,"url":null,"abstract":"It is known that we can always 3-triangulate (i.e. divide into tetrahedra with the original vertices) convex polyhedra but not always non-convex ones. Polyhedra topologically equivalent to ball with p handles, shortly p-toroids, cannot be convex. So, it is interesting to investigate possibilities and properties of their 3-triangulations. Here we study the minimal number of necessary tetrahedra for the triangulation of a 3-triangulable p-toroid. For that purpose, we developed the concept of piecewise convex polyhedron and that of its connection graph.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimal 3-triangulations of p-toroids\",\"authors\":\"M. Stojanovic\",\"doi\":\"10.2298/fil2301115s\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is known that we can always 3-triangulate (i.e. divide into tetrahedra with the original vertices) convex polyhedra but not always non-convex ones. Polyhedra topologically equivalent to ball with p handles, shortly p-toroids, cannot be convex. So, it is interesting to investigate possibilities and properties of their 3-triangulations. Here we study the minimal number of necessary tetrahedra for the triangulation of a 3-triangulable p-toroid. For that purpose, we developed the concept of piecewise convex polyhedron and that of its connection graph.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2298/fil2301115s\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/fil2301115s","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is known that we can always 3-triangulate (i.e. divide into tetrahedra with the original vertices) convex polyhedra but not always non-convex ones. Polyhedra topologically equivalent to ball with p handles, shortly p-toroids, cannot be convex. So, it is interesting to investigate possibilities and properties of their 3-triangulations. Here we study the minimal number of necessary tetrahedra for the triangulation of a 3-triangulable p-toroid. For that purpose, we developed the concept of piecewise convex polyhedron and that of its connection graph.