Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles-I

The study of dihedral f-tilings of the Euclidean sphere S 2 by triangles and rsided regular polygons was initiated in 2004 where the case r = 4 was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and r-sided regular polygons, for any r 5, was described. Later on, in [3], the classication of all f-tilings of S 2 whose prototiles are an equilateral triangle and an isosceles triangle is obtained. The algebraic and combinatorial description of spherical f-tilings by equilateral triangles and scalene triangles of angles , and ( > > ) whose edge adjacency is performed by the side opposite to was done in [4]. In this paper we extend these results considering the edge adjacency performed by the side opposite to .