Geometric and combinatorial structure of a class of spherical folding tesselations - II

The classification of the dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was recently achieved. In this paper we complete the classification of spherical folding tessellations by kites and scalene triangles, where the shorter side of the kite is equal to the longest side of the triangle, initiated in [C.P. Avelino and A.F. Santos, Czech. Math. J. (to appear)]. The combinatorial structure of each tiling is also analyzed.