Tilings of the sphere by congruent pentagons III: Edge combination a5

Yohji Akama; Erxiao Wang; Min Yan

doi:10.1016/j.aim.2021.107881

Tilings of the sphere by congruent pentagons III: Edge combination a⁵

Yohji Akama, Erxiao Wang, Min Yan

SCI - Mathematics

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

Abstract

There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map tiling with 20 tiles.

Original language	English
Article number	107881
Journal	Advances in Mathematics
DOIs	https://doi.org/10.1016/j.aim.2021.107881
Publication status	Accepted/In press - 2021

Keywords

Classification
Pentagon
Spherical tiling

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/j.aim.2021.107881

Cite this

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title = "Tilings of the sphere by congruent pentagons III: Edge combination a5",

abstract = "There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map tiling with 20 tiles.",

keywords = "Classification, Pentagon, Spherical tiling",

author = "Yohji Akama and Erxiao Wang and Min Yan",

note = "Funding Information: Research was supported by ZJNU Shuang-Long Distinguished Professorship Fund No. YS304319159.Research was supported by Hong Kong RGC General Research Fund 16303515 and 16305920. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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language = "English",

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AU - Yan, Min

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N2 - There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map tiling with 20 tiles.

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KW - Classification

KW - Pentagon

KW - Spherical tiling

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