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Tilings of the sphere by congruent quadrilaterals III: Edge combination a 3 b with general angles

  • Yixi Liao ORCID logo , Pinren Qian , Erxiao Wang ORCID logo EMAIL logo and Yingyun Xu
Published/Copyright: January 3, 2024

Abstract

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 3 b -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.

MSC 2020: 52C20; 05B45

Communicated by Manfred Droste


Award Identifier / Grant number: LZ22A010003

Award Identifier / Grant number: YS304319159

Funding statement: The research was supported by Key projects of Zhejiang Natural Science Foundation (Grant No. LZ22A010003) and ZJNU Shuang-Long Distinguished Professorship Fund (Grant No. YS304319159).

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Received: 2023-06-03
Published Online: 2024-01-03
Published in Print: 2024-09-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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