S2 coverings by isosceles and scalene triangles – adjacency case II

Abstract

The aim of this paper is to complete the study and classification of spherical f-tilings by scalene triangles T and isosceles triangles T′ within a subclass defined by the adjacency of the lower side of T and the longest side of T′. It consists of eight families of f-tilings (two families with one continuous parameter, one family with one discrete parameter and one continuous parameter, and five families with one discrete parameter). We also analyze the combinatorial structure of all these families of f-tilings, as well as the group of symmetries of each tiling; the transitivity classes of isogonality are included.