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

Institute of Software Engineering and Artificial Intelligence (7160)

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

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
Pages (from-to)	1-14
Number of pages	14
Journal	Computational Geometry
Volume	93
DOIs	https://doi.org/10.1016/j.comgeo.2020.101700
Publication status	Published - 2021

Keywords

Folding
Origami folding
Cube
Polyomino with holes
Non-simple polyomino

ASJC Scopus subject areas

Computational Mathematics
Control and Optimization
Geometry and Topology
Computer Science Applications
Computational Theory and Mathematics

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1016/j.comgeo.2020.101700

http://www.sciencedirect.com/science/article/pii/S0925772120300948

Cite this

@article{1e06e5fec202468bb9e426e651f3c4aa,

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

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",

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

language = "English",

volume = "93",

pages = "1--14",

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

Y1 - 2021

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 - Folding

KW - Origami folding

KW - Cube

KW - Polyomino with holes

KW - Non-simple polyomino

UR - https://arxiv.org/abs/1910.09917

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

U2 - 10.1016/j.comgeo.2020.101700

DO - 10.1016/j.comgeo.2020.101700

M3 - Article

SN - 0925-7721

VL - 93

SP - 1

EP - 14

JO - Computational Geometry

JF - Computational Geometry

M1 - 101700

ER -

Folding polyominoes with holes into a cube

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

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Cite this