Unfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered Squares

• Zachary, Abel

• Brad, Ballinger

• Erik, D. Demaine

• Martin, L. Demaine

• Jeff, Erickson

• Adam, Hesterberg

• Hiro, Ito

• Irina, Kostitsyna

• Jayson, Lynch

• Ryuhei, Uehara

抄録

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------------------------------

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------------------------------

収録刊行物

• 情報処理学会論文誌

  情報処理学会論文誌 58 (8), 2017-08-15

キーワード

• [特集：離散と計算の幾何・グラフ・ゲーム] dissection, folding and unfolding, polyomino, rep-cube, rep-tile

詳細情報

• CRID: 1050564287861863680
• NII論文ID: 170000148837
• NII書誌ID: AN00116647
• ISSN: 18827764
• Web Site: http://id.nii.ac.jp/1001/00182911/
• 本文言語コード: en
• 資料種別: journal article
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