Erik D. Demaine , Martin L. Demaine , Ryuhei Uehara
{"title":"Developing a tetramonohedron with minimum cut length","authors":"Erik D. Demaine , Martin L. Demaine , Ryuhei Uehara","doi":"10.1016/j.comgeo.2022.101903","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the way of unfolding a given tetramonohedron, which is a tetrahedron<span> that consists of four congruent triangles<span>. Our aim is finding a way that achieves the minimum cut length to develop it. We first show the rigorous way to unfold any given tetramonohedron with minimum cut length. Next, we focus on a family of tetramonohedra that consist of four congruent isosceles triangles. For this family, we apply our result and investigate their behavior.</span></span></p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Geometry-Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0925772122000463","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate the way of unfolding a given tetramonohedron, which is a tetrahedron that consists of four congruent triangles. Our aim is finding a way that achieves the minimum cut length to develop it. We first show the rigorous way to unfold any given tetramonohedron with minimum cut length. Next, we focus on a family of tetramonohedra that consist of four congruent isosceles triangles. For this family, we apply our result and investigate their behavior.
期刊介绍:
Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems.
Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.