论文标题
球体的斜利通过一致的四边形II：边缘组合$ a^3 b $带有理性角度
Tilings of the sphere by congruent quadrilaterals II: edge combination $a^3 b$ with rational angles
论文作者
论文摘要
一致的四边形通过一致的四个论文完全分类的球体的边缘到边缘砖。第二个使用三角二芬太汀方程的强大工具来对$ a^3b $ - Quadrilefirals的情况进行分类，各个角度都是理性的。有$ 12 $零星的零星和$ 3 $无限的四边形序列，承认$ 2 $ - 莱er地球地图瓷砖及其修改，以及$ 3 $零星的四边形，承认$ 4 $ $ 4 $。其中只有$ 3 $四边形是凸。作为副产品，获得了新的有趣的非边缘到边缘三角形砖。
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 $2$-layer earth map tilings together with their modifications, and $3$ sporadic quadrilaterals admitting $4$ exceptional tilings. Among them only $3$ quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.
