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 Technology (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

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10.1016/j.comgeo.2020.101700

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

Cite this

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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 - http://www.scopus.com/inward/record.url?scp=85089476554&partnerID=8YFLogxK

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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