Spherical f-Tilings by (Equilateral and Isosceles) Triangles and Isosceles Trapezoids

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.