Dihedral f-tilings of the sphere by equilateral and scalene triangles. III. (Q1010884)

Summary: The study of spherical dihedral f-tilings by equilateral and isosceles triangles was introduced in [\textit{A. M. d'Azevedo Breda, P. S. Ribeiro} and \textit{A. F. Santos} Eur. J. Comb. 30, No. 1, 119--132 (2009; Zbl 1161.52014)]. Taking as prototiles equilateral and scalene triangles, we are faced with three possible ways of adjacency. In part I and II of this paper [\textit{A. M. d'Azevedo Breda, P. S. Ribeiro} and \textit{A. F. Santos}, part I, and part II in Electron. J. Comb. 15, No. 1, Research Paper R91, 21 p. (2008; Zbl 1161.52003)] two of these possibilities were studied. Here, we complete this study, describing the f-tilings related to the remaining case of adjacency, including their symmetry groups. A table summarizing the results concerning all dihedral f-tilings by equilateral and scalene triangles is given in Table 2.