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

Institut für Softwaretechnologie (7160)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Aufsatznummer	101700
Seiten (von - bis)	1-14
Seitenumfang	14
Fachzeitschrift	Computational Geometry
Jahrgang	93
DOIs	https://doi.org/10.1016/j.comgeo.2020.101700
Publikationsstatus	Veröffentlicht - 2021

ASJC Scopus subject areas

Computational Mathematics
Steuerung und Optimierung
Geometrie und Topologie
Angewandte Informatik
Theoretische Informatik und Mathematik

Fields of Expertise

Information, Communication & Computing

Zugriff auf Dokument

10.1016/j.comgeo.2020.101700

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

Andere Dateien und Links

Dieses zitieren

@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 - 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

ASJC Scopus subject areas

Fields of Expertise

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Dieses zitieren