Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II - Breda, A. M. d'Azevedo; Ribeiro, Patrícia S.; Santos, Altino F. (The Electronic Journal of Combinatorics, 2008)
The study of dihedral f-tilings of the Euclidean sphere $S^2$ by triangles and $r$-sided 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 $r\ge 5$, was described. Later on, in [3], the classification 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 $β$, $γ$ and $δ$ $(β>γ>δ)$ whose edge adjacency is performed by the side opposite to $β$ was done in [4]. In this paper we extend these results considering the edge adjacency performed by the side opposite to $δ$.