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Tilings of the sphere by congruent quadrilaterals III: edge combination $a^3b$ with general angles (2206.15342v3)
Published 30 Jun 2022 in math.CO and math.MG
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 $a3b$-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.