Paper by Erik D. Demaine

Zachary Abel, Brad Ballinger, Erik D. Demaine, Martin L. Demaine, Jeff Erickson, Adam Hesterberg, Hiro Ito, Irina Kostitsyna, Jayson Lynch, and Ryuhei Uehara, “Unfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered Squares”, Journal of Information Processing, volume 25, August 2017, pages 610–615.

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.

The paper is 6 pages.

The paper is available in PDF (545k).
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Related papers:
RepCube_JCDCGGG2016 (Unfolding and Dissection of Multiple Cubes)

See also other papers by Erik Demaine.
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Last updated April 22, 2019 by Erik Demaine.