2024-03-28T21:59:01Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:001829992022-10-21T05:24:51Z00581:08997:09006
Unfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered SquaresUnfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered Squareseng[特集:離散と計算の幾何・グラフ・ゲーム] dissection, folding and unfolding, polyomino, rep-cube, rep-tilehttp://id.nii.ac.jp/1001/00182911/Journal Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=182999&item_no=1&attribute_id=1&file_no=1Copyright (c) 2017 by the Information Processing Society of JapanMathematics Department, MITDepartment of Mathematics, Humboldt State UniversityComputer Science and Artificial Intelligence Laboratory, MITComputer Science and Artificial Intelligence Laboratory, MITDepartment of Computer Science, University of Illinois at Urbana-ChampaignComputer Science and Artificial Intelligence Laboratory, MITGraduate School of Informatics and Engineering, the University of Electro-CommunicationsComputer Science Department, Université libre de BruxellesComputer Science and Artificial Intelligence Laboratory, MITSchool of Information Science, Japan Advanced Institute of Science and TechnologyZachary, AbelBrad, BallingerErik, D. DemaineMartin, L. DemaineJeff, EricksonAdam, HesterbergHiro, ItoIrina, KostitsynaJayson, LynchRyuhei, UeharaIn this paper, we introduce the notion of “rep-cube”: a net of a cube that can be divided into multiple polygons, each of which can be folded into a cube. This notion is inspired by the notion of polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infinitely many distinct rep-cubes. We also extend this notion to doubly covered squares and regular tetrahedra.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.25(2017) (online)DOI http://dx.doi.org/10.2197/ipsjjip.25.610------------------------------In this paper, we introduce the notion of “rep-cube”: a net of a cube that can be divided into multiple polygons, each of which can be folded into a cube. This notion is inspired by the notion of polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infinitely many distinct rep-cubes. We also extend this notion to doubly covered squares and regular tetrahedra.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.25(2017) (online)DOI http://dx.doi.org/10.2197/ipsjjip.25.610------------------------------AN00116647情報処理学会論文誌5882017-08-151882-77642017-08-10