Paper by Erik D. Demaine

Reference:

Kingston Yao Czajkowski, Erik D. Demaine, Martin L. Demaine, Kim Eppling, Robby Kraft, Klara Mundilova, and Levi Smith, “Folding Small Polyominoes into a Unit Cube”, in Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020), Saskatchewan, Saskatoon, Canada, August 5–7, 2020.

BibTeX

@InProceedings{CubeFolding_CCCG2020,
  AUTHOR        = {Kingston Yao Czajkowski and Erik D. Demaine and Martin L. Demaine and Kim Eppling and Robby Kraft and Klara Mundilova and Levi Smith},
  TITLE         = {Folding Small Polyominoes into a Unit Cube},
  BOOKTITLE     = {Proceedings of the 32nd Canadian Conference in Computational Geometry (CCCG 2020)},
  bookurl       = {http://vga.usask.ca/cccg2020/},
  ADDRESS       = {Saskatchewan, Saskatoon, Canada},
  MONTH         = {August 5--7},
  YEAR          = 2020,

  withstudent   = 1,
  unrefereed    = 1,
  dblp          = {https://dblp.org/rec/conf/cccg/CzajkowskiDDEKM20},
  comments      = {My presentation is available on <A HREF="https://youtu.be/o-Te14RDZJE">YouTube</A>.},
  papers        = {CubeFoldingHoles_CGTA; PolyformFolding_IJCGA},
}

Abstract:

We demonstrate that a 3 × 3 square can fold into a unit cube using horizontal, vertical, and diagonal creases on the 6 × 6 half-grid. Together with previous results, this result implies that all tree-shaped polyominoes with at least nine squares fold into a unit cube. We also make partial progress on the analogous problem for septominoes and octominoes by showing a half-grid folding of the U septomino and 2 × 4 rectangle into a unit cube.

Comments:

My presentation is available on YouTube.

Availability:

The paper is available in PDF (749k).

See information on file formats.

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Related papers:

CubeFoldingHoles_CGTA (Folding Polyominoes with Holes into a Cube)

PolyformFolding_IJCGA (Folding Polyominoes into (Poly)Cubes)