Tilings of the Sphere by Congruent Quadrilaterals I: Edge Combination a2bc.

Edge-to-edge tilings of the sphere by congruent a2bc-quadrilaterals are classified as 3 classes: (1) A 1-parameter family of quadrilateral subdivisions of the octahedron with 24 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. [ABSTRACT FROM AUTHOR]