Tilings of the sphere by congruent quadrilaterals III: edge combination \(a^3b\) with general angles

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of \(a^3b\)-quadrilaterals with some irrational angle: there are a sequence of \(1\)-parameter families of quadrilaterals admitting \(2\)-layer eart...

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Bibliographic Details
Published inarXiv.org
Main Authors Liao, Yixi, Qian, Pinren, Wang, Erxiao, Xu, Yingyun
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.06.2023
Subjects
Quadrilaterals
Tiling
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Summary:Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of \(a^3b\)-quadrilaterals with some irrational angle: there are a sequence of \(1\)-parameter families of quadrilaterals admitting \(2\)-layer earth map tilings together with their basic flip modifications under extra condition, and \(5\) sporadic quadrilaterals each admitting a special tiling. A summary of the full classification is presented in the end.
ISSN:2331-8422