Folding polyominoes with holes into a cube

Oswin Aichholzer; Hugo A. Akitaya; Kenneth C. Cheung; Erik D. Demaine; Martin L. Demaine; Sándor P. Fekete; Linda Kleist; Irina Kostitsyna; Maarten Löffler; Zuzana Masárová; Klara Mundilova; Christiane Schmidt

doi:10.1016/j.comgeo.2020.101700

Folding polyominoes with holes into a cube

Oswin Aichholzer
, Hugo A. Akitaya
, Kenneth C. Cheung
, Erik D. Demaine
, Martin L. Demaine
, Sándor P. Fekete
, Linda Kleist
, Irina Kostitsyna
, Maarten Löffler
, Zuzana Masárová
, Klara Mundilova
, Christiane Schmidt (Corresponding author)

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

Abstract

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 one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.

Original language	English
Article number	101700
Number of pages	14
Journal	Computational Geometry
Volume	93
DOIs	https://doi.org/10.1016/j.comgeo.2020.101700
Publication status	Published - Feb 2021

Funding

This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615 . Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31 .

Funders	Funder number
National Science Foundation	CCF-1422311
Directorate for Computer and Information Science and Engineering	1423615, 1422311
Austrian Science Fund	342-N31

Keywords

Cube
Folding
Non-simple polyomino
Origami folding
Polyomino with holes

Access to Document

10.1016/j.comgeo.2020.101700

Cite this

@article{6d996693aec248b79a83559361227623,

title = "Folding polyominoes with holes into a cube",

abstract = "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 one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.",

keywords = "Cube, Folding, Non-simple polyomino, Origami folding, Polyomino with holes",

author = "Oswin Aichholzer and Akitaya, \{Hugo A.\} and Cheung, \{Kenneth C.\} and Demaine, \{Erik D.\} and Demaine, \{Martin L.\} and Fekete, \{S{\'a}ndor P.\} and Linda Kleist and Irina Kostitsyna and Maarten L{\"o}ffler and Zuzana Mas{\'a}rov{\'a} and Klara Mundilova and Christiane Schmidt",

year = "2021",

month = feb,

doi = "10.1016/j.comgeo.2020.101700",

language = "English",

volume = "93",

journal = "Computational Geometry",

issn = "0925-7721",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Folding polyominoes with holes into a cube

AU - Aichholzer, Oswin

AU - Akitaya, Hugo A.

AU - Cheung, Kenneth C.

AU - Demaine, Erik D.

AU - Demaine, Martin L.

AU - Fekete, Sándor P.

AU - Kleist, Linda

AU - Kostitsyna, Irina

AU - Löffler, Maarten

AU - Masárová, Zuzana

AU - Mundilova, Klara

AU - Schmidt, Christiane

PY - 2021/2

Y1 - 2021/2

N2 - 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 one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.

AB - 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 one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.

KW - Cube

KW - Folding

KW - Non-simple polyomino

KW - Origami folding

KW - Polyomino with holes

UR - https://www.scopus.com/pages/publications/85089476554

U2 - 10.1016/j.comgeo.2020.101700

DO - 10.1016/j.comgeo.2020.101700

M3 - Article

AN - SCOPUS:85089476554

SN - 0925-7721

VL - 93

JO - Computational Geometry

JF - Computational Geometry

M1 - 101700

ER -

Folding polyominoes with holes into a cube

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this