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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| 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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| AbstractList | 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. |
| Author | Wang, Erxiao Xu, Yingyun Liao, Yixi Qian, Pinren |
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