{"title":"An explicit PL-embedding of the square flat torus into $\\mathbb{E}^3$","authors":"Tanessí Quintanar","doi":"10.20382/JOCG.V11I1A24","DOIUrl":null,"url":null,"abstract":"We present an explicit PL-embedding of the flat square torus $\\mathbb{T}^2=\\mathbb{E}^2/\\mathbb{Z}^2$ into $\\mathbb{E}^3$, with 40 vertices and 80 faces.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"30 1","pages":"615-628"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computational Geometry & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20382/JOCG.V11I1A24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We present an explicit PL-embedding of the flat square torus $\mathbb{T}^2=\mathbb{E}^2/\mathbb{Z}^2$ into $\mathbb{E}^3$, with 40 vertices and 80 faces.
期刊介绍：
The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms.
Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.
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