Spherical f-tilings by two non congruent classes of isosceles triangles - I (Q2915728)

Dihedral f-tilings are edge-to-edge decompositions of the sphere by geodesic polygons which are congruent to one of two non congruent isosceles triangles such that all vertices satisfy the angle folding relation. The paper gives a classification of dihedral f-tilings with adjacency of type I by three parametrized families and one isolated tiling, and provides combinatorial structure of each tiling including the symmetry group. It extends the classification of dihedral spherical f-tilings for which one of the prototiles is an equilateral triangle.