Tilings of the Sphere by Congruent Quadrilaterals I:Edge Combination a^(2)bc  

作　　者：Yixi LIAO Pinren QIAN Erxiao WANG Yingyun XU 

机构地区：[1]School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,Zhejiang,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第5期733-766,共34页数学年刊（B辑英文版）

基　　金：supported by the Key Projects of Zhejiang Natural Science Foundation(No.LZ22A010003);ZJNU Shuang-Long Distinguished Professorship Fund(No.YS304319159)。

摘　　要：Edge-to-edge tilings of the sphere by congruent a^(2)bc-quadrilaterals are classified as 3 classes:(1)A 1-parameter family of quadrilateral subdivisions of the octahedron with24 tiles,and a flip modification for one special parameter;(2)a 2-parameter family of 2-layer earth map tilings with 2n tiles for each n≥3;(3)a 3-layer earth map tiling with 8n tiles for each n≥2,and two flip modifications for each odd n.The authors also describe the moduli of parameterized tilings and provide the full geometric data for all tilings.

关 键 词：Spherical tiling QUADRILATERAL Classification Earth map tiling SUBDIVISION 

分 类 号：TU12[建筑科学—建筑理论]