Paper by Erik D. Demaine

Reference:

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.

BibTeX

@Article{RepCube_JIP,
  AUTHOR        = {Zachary Abel and Brad Ballinger and Erik D. Demaine and Martin L. Demaine and Jeff Erickson and Adam Hesterberg and Hiro Ito and Irina Kostitsyna and Jayson Lynch and Ryuhei Uehara},
  TITLE         = {Unfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered Squares},
  JOURNAL       = {Journal of Information Processing},
  journalurl    = {http://www.ipsj.or.jp/english/jip/},
  VOLUME        = 25,
  MONTH         = {August},
  YEAR          = 2017,
  PAGES         = {610--615},

  length        = {6 pages},
  withstudent   = 1,
  papers        = {RepCube_JCDCGGG2016},
  replaces      = {RepCube_JCDCGGG2016},
  doi           = {https://dx.doi.org/10.2197/ipsjjip.25.610},
  dblp          = {https://dblp.org/rec/journals/jip/AbelBDD0HIKLU17},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.2197/ipsjjip.25.610">J-STAGE</A>.},
}

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.

Comments:

This paper is also available from J-STAGE.

Length:

The paper is 6 pages.

Availability:

The paper is available in PDF (545k).

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Related papers:

RepCube_JCDCGGG2016 (Unfolding and Dissection of Multiple Cubes)