A class of spherical folding subdivisions

The classification of the dihedral folding tesselations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent papers. In this paper we extend this classification to scalene triangles, presenting all the dihedral folding tesselations of the sphere by kites and scalene triangles in which the longest side of the kite is equal to the lower side of the triangle