---
_id: '6989'
abstract:
- lang: eng
  text: 'When can a polyomino piece of paper be folded into a unit cube? Prior work
    studied tree-like polyominoes, but polyominoes with holes remain an intriguing
    open problem. We present sufficient conditions for a polyomino with hole(s) to
    fold into a cube, and conditions under which cube folding is impossible. In particular,
    we show that all but five special simple holes guarantee foldability. '
acknowledgement: This research was performed in part at the 33rd Bellairs Winter Workshop
  on Computational  Geometry. We thank all other participants for a fruitful atmosphere.
article_processing_charge: No
arxiv: 1
author:
- first_name: Oswin
  full_name: Aichholzer, Oswin
  last_name: Aichholzer
- first_name: Hugo A
  full_name: Akitaya, Hugo A
  last_name: Akitaya
- first_name: Kenneth C
  full_name: Cheung, Kenneth C
  last_name: Cheung
- first_name: Erik D
  full_name: Demaine, Erik D
  last_name: Demaine
- first_name: Martin L
  full_name: Demaine, Martin L
  last_name: Demaine
- first_name: Sandor P
  full_name: Fekete, Sandor P
  last_name: Fekete
- first_name: Linda
  full_name: Kleist, Linda
  last_name: Kleist
- first_name: Irina
  full_name: Kostitsyna, Irina
  last_name: Kostitsyna
- first_name: Maarten
  full_name: Löffler, Maarten
  last_name: Löffler
- first_name: Zuzana
  full_name: Masárová, Zuzana
  id: 45CFE238-F248-11E8-B48F-1D18A9856A87
  last_name: Masárová
  orcid: 0000-0002-6660-1322
- first_name: Klara
  full_name: Mundilova, Klara
  last_name: Mundilova
- first_name: Christiane
  full_name: Schmidt, Christiane
  last_name: Schmidt
citation:
  ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes
    into a cube. In: <i>Proceedings of the 31st Canadian Conference on Computational
    Geometry</i>. Canadian Conference on Computational Geometry; 2019:164-170.'
  apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M.
    L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a
    cube. In <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>
    (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.'
  chicago: Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin
    L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes
    into a Cube.” In <i>Proceedings of the 31st Canadian Conference on Computational
    Geometry</i>, 164–70. Canadian Conference on Computational Geometry, 2019.
  ieee: O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,”
    in <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>,
    Edmonton, Canada, 2019, pp. 164–170.
  ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist
    L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding
    polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference
    on Computational Geometry. CCCG: Canadian Conference in Computational Geometry,
    164–170.'
  mla: Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Proceedings
    of the 31st Canadian Conference on Computational Geometry</i>, Canadian Conference
    on Computational Geometry, 2019, pp. 164–70.
  short: O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P.
    Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt,
    in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian
    Conference on Computational Geometry, 2019, pp. 164–170.
conference:
  end_date: 2019-08-10
  location: Edmonton, Canada
  name: 'CCCG: Canadian Conference in Computational Geometry'
  start_date: 2019-08-08
date_created: 2019-11-04T16:46:11Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2026-06-18T19:14:37Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
external_id:
  arxiv:
  - '1910.09917'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://sites.ualberta.ca/~cccg2019/cccg2019_proceedings.pdf
month: '08'
oa: 1
oa_version: Published Version
page: 164-170
publication: Proceedings of the 31st Canadian Conference on Computational Geometry
publication_status: published
publisher: Canadian Conference on Computational Geometry
quality_controlled: '1'
related_material:
  record:
  - id: '8317'
    relation: extended_version
    status: public
scopus_import: '1'
status: public
title: Folding polyominoes with holes into a cube
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...