Spherical f-tilings by two noncongruent classes of isosceles triangles-II

In this work, we give a complete classification of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles with certain adjacency pattern. As it will be shown, this class is composed by two discrete families denoted by {ie.}m, m . 2, m . ., F k, k . 4, k . . and two sporadic tilings denoted by G and H.