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Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons? / Arseneva, Elena; Langerman, Stefan.

In: Graphs and Combinatorics, Vol. 36, No. 2, 01.03.2020, p. 339-345.

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

Harvard

Arseneva, E & Langerman, S 2020, 'Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons?', Graphs and Combinatorics, vol. 36, no. 2, pp. 339-345. https://doi.org/10.1007/s00373-019-02105-3

APA

Arseneva, E., & Langerman, S. (2020). Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons? Graphs and Combinatorics, 36(2), 339-345. https://doi.org/10.1007/s00373-019-02105-3

Vancouver

Arseneva E, Langerman S. Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons? Graphs and Combinatorics. 2020 Mar 1;36(2): 339-345. https://doi.org/10.1007/s00373-019-02105-3

Author

Arseneva, Elena ; Langerman, Stefan. / Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons?. In: Graphs and Combinatorics. 2020 ; Vol. 36, No. 2. pp. 339-345.

BibTeX

@article{12c9c428e2a841a7b351b8692cd83394,
title = "Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons?",
abstract = "Which convex 3D polyhedra can be obtained by gluing several regular hexagons edge-to-edge? It turns out that there are only 15 possible types of shapes, 5 of which are doubly-covered 2D polygons. We give examples for most of them, including all simplicial and all flat shapes, and give a characterization for the latter ones. It is open whether the remaining can be realized.",
keywords = "Alexandrov{\textquoteright}s theorem, Gluings, Polyhedral metrics, Regular polygons, Alexandrov's theorem",
author = "Elena Arseneva and Stefan Langerman",
year = "2020",
month = mar,
day = "1",
doi = "10.1007/s00373-019-02105-3",
language = "English",
volume = "36",
pages = " 339--345",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons?

AU - Arseneva, Elena

AU - Langerman, Stefan

PY - 2020/3/1

Y1 - 2020/3/1

N2 - Which convex 3D polyhedra can be obtained by gluing several regular hexagons edge-to-edge? It turns out that there are only 15 possible types of shapes, 5 of which are doubly-covered 2D polygons. We give examples for most of them, including all simplicial and all flat shapes, and give a characterization for the latter ones. It is open whether the remaining can be realized.

AB - Which convex 3D polyhedra can be obtained by gluing several regular hexagons edge-to-edge? It turns out that there are only 15 possible types of shapes, 5 of which are doubly-covered 2D polygons. We give examples for most of them, including all simplicial and all flat shapes, and give a characterization for the latter ones. It is open whether the remaining can be realized.

KW - Alexandrov’s theorem

KW - Gluings

KW - Polyhedral metrics

KW - Regular polygons

KW - Alexandrov's theorem

UR - http://www.scopus.com/inward/record.url?scp=85074476760&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/convex-polyhedra-made-gluing-regular-hexagons

UR - https://www.mendeley.com/catalogue/49ae2d0b-1900-3950-a746-81d276dd683a/

U2 - 10.1007/s00373-019-02105-3

DO - 10.1007/s00373-019-02105-3

M3 - Article

AN - SCOPUS:85074476760

VL - 36

SP - 339

EP - 345

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 2

ER -

ID: 48856212