Spherical f-tilings by scalene triangles and isosceles trapezoids, I

The study of the dihedral f-tilings of the sphere S2S2 whose prototiles are an equilateral or isosceles triangle and an isosceles trapezoid was described in [C.P. Avelino, A.F. Santos, Spherical f-tilings by (equilateral and isosceles) triangles and isosceles trapezoids, 2008 (submitted for publication)]. In this paper we generalize this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in some cases of adjacency.