Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals

Hoi Ping Luk; Ho Man Cheung

doi:10.1007/s00026-023-00685-9

Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals

Hoi Ping Luk^*, Ho Man Cheung

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a³b). Parallel to a complete classification by Cheung, Luk, and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for the tilings.

Original language	English
Pages (from-to)	485-527
Number of pages	43
Journal	Annals of Combinatorics
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s00026-023-00685-9
Publication status	Published - Jun 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

05B45
11Y50
51M09
52C20
Classification
Diophantine analysis
Quadrilateral
Rational angles
Spherical tilings
Spherical trigonometry

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10.1007/s00026-023-00685-9

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title = "Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals",

abstract = "We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete classification by Cheung, Luk, and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for the tilings.",

keywords = "05B45, 11Y50, 51M09, 52C20, Classification, Diophantine analysis, Quadrilateral, Rational angles, Spherical tilings, Spherical trigonometry",

author = "Luk, \{Hoi Ping\} and Cheung, \{Ho Man\}",

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doi = "10.1007/s00026-023-00685-9",

language = "English",

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TY - JOUR

T1 - Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals

AU - Luk, Hoi Ping

AU - Cheung, Ho Man

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/6

Y1 - 2024/6

N2 - We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete classification by Cheung, Luk, and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for the tilings.

AB - We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete classification by Cheung, Luk, and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for the tilings.

KW - 05B45

KW - 11Y50

KW - 51M09

KW - 52C20

KW - Classification

KW - Diophantine analysis

KW - Quadrilateral

KW - Rational angles

KW - Spherical tilings

KW - Spherical trigonometry

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001186177700001

UR - https://openalex.org/W4392916202

UR - https://www.scopus.com/pages/publications/85188135920

U2 - 10.1007/s00026-023-00685-9

DO - 10.1007/s00026-023-00685-9

M3 - Journal Article

SN - 0218-0006

VL - 28

SP - 485

EP - 527

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 2

ER -

Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals

Abstract

Bibliographical note

Keywords

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