{"title":"Edge-Unfolding Polycubes with Orthogonally Convex Layers","authors":"Mirela Damian, Henk Meijer","doi":"arxiv-2407.01326","DOIUrl":null,"url":null,"abstract":"A polycube is an orthogonal polyhedron composed of unit cubes glued together\nalong entire faces, homeomorphic to a sphere. A polycube layer is the section\nof the polycube that lies between two horizontal cross-sections of the polycube\nat unit distance from each other. An edge unfolding of a polycube involves\ncutting its surface along any of the constituent cube edges and flattening it\ninto a single, non-overlapping planar piece. We show that any polycube with\northogonally convex layers can be edge unfolded.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.01326","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
A polycube is an orthogonal polyhedron composed of unit cubes glued together
along entire faces, homeomorphic to a sphere. A polycube layer is the section
of the polycube that lies between two horizontal cross-sections of the polycube
at unit distance from each other. An edge unfolding of a polycube involves
cutting its surface along any of the constituent cube edges and flattening it
into a single, non-overlapping planar piece. We show that any polycube with
orthogonally convex layers can be edge unfolded.
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