The classification of dihedral folding tessellations of the sphere and the plane whose prototiles are a kite and an equilateral triangle are obtained in a recent paper, [1]. In this paper, we extend this classification presenting all the dihedral folding tessellations of the sphere by kites and isosceles triangles in a particular case of adjacency. A list containing these tilings including its combinatorial structure is presented in Table 1.

CEMAT - Center for Computational and Stochastic Mathematics