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arXiv · 2206.15342

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

Yixi Liao·Pinren Qian·Erxiao Wang·Yingyun Xu
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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 $a^3b$-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.

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Yixi Liao, Pinren Qian, Erxiao Wang, Yingyun Xu. 2022-06-30. Tilings of the sphere by congruent quadrilaterals III: edge combination $a^3b$ with general angles. https://arxiv.org/abs/2206.15342

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