Spherical F-Tilings by Triangles and r-Sided Regular Polygons, r >= 5

The study of dihedral f-tilings of the sphere S2 by spherical triangles and equiangular spherical quadrangles (which includes the case of 4-sided regular polygons) was presented in [3]. Also, in [6], the study of dihedral f-tilings of S2 whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scalene triangles as the prototiles will lead to a wide family of f-tilings). In this paper we extend these results, presenting the study of dihedral f-tilings by spherical triangles and r-sided regular polygons, for any r ≥ 5. The combinatorial structure, including the symmetry group of each tiling, is given in Table 1.