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

Avelino, Catarina P.; Santos, Altino F.

European Journal of Combinatorics, 30(5) (2009), 1221-1244

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.