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Spherical f-tilings by (equilateral and isosceles) triangles and isosceles trapezoids

Avelino, Catarina P.; Santos, Altino F.

Annals of Combinatorics, 15(4) (2011), 565-596

Dihedral f-tilings by spherical parallelograms and spherical triangles were obtained in [3–5]. In this paper we extend these results presenting the study of all dihedral f-tilings of the sphere S 2, whose prototiles are a spherical equilateral or isosceles triangle and a spherical isosceles trapezoid. The combinatorial structure, including the symmetry group of each tiling, is given in Table 1.