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TILINGS OF THE SPHERE BY CONGRUENT QUADRILATERALS II: EDGE COMBINATION $a^3b$ WITH RATIONAL ANGLES
Published online by Cambridge University Press: 07 September 2023
Abstract
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of $a^3b$-quadrilaterals with all angles being rational degrees. There are $12$ sporadic and $3$ infinite sequences of quadrilaterals admitting the two-layer earth map tilings together with their modifications, and $3$ sporadic quadrilaterals admitting $4$ exceptional tilings. Among them only three quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
Footnotes
This research was supported by key projects of Zhejiang Natural Science Foundation No. LZ22A010003 and ZJNU Shuang-Long Distinguished Professorship Fund No. YS304319159.
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