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

doi:10.2197/ipsjjip.25.610

Zachary Abel, Brad Ballinger, Erik D. Demaine, Martin L. Demaine, Jeff Erickson, Adam Hesterberg, Hiro Ito, Irina Kostitsyna, Jayson Lynch, Ryuhei Uehara

Author information

Zachary Abel
Mathematics Department, MIT
Brad Ballinger
Department of Mathematics, Humboldt State University
Erik D. Demaine
Computer Science and Artificial Intelligence Laboratory, MIT
Martin L. Demaine
Computer Science and Artificial Intelligence Laboratory, MIT
Jeff Erickson
Department of Computer Science, University of Illinois at Urbana-Champaign
Adam Hesterberg
Computer Science and Artificial Intelligence Laboratory, MIT
Hiro Ito
Graduate School of Informatics and Engineering, the University of Electro-Communications
Irina Kostitsyna
Computer Science Department, Université libre de Bruxelles
Jayson Lynch
Computer Science and Artificial Intelligence Laboratory, MIT
Ryuhei Uehara
School of Information Science, Japan Advanced Institute of Science and Technology

Keywords: dissection, folding and unfolding, polyomino, rep-cube, rep-tile

JOURNAL FREE ACCESS

2017 Volume 25 Pages 610-615

DOI https://doi.org/10.2197/ipsjjip.25.610

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Abstract

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.

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