Right Triangular Dihedral \(f\)-Tilings of the Sphere: \((\alpha,\beta,\frac{\pi}{2})\) and \((\gamma,\gamma,\frac{\pi}{2})\)

Abstract

The classification of all dihedral f-tilings of the Riemannian sphere \(S^2\) ,whose prototiles are two right triangles with at least one isosceles, is given.The combinatorial structure and the symmetry group of each tiling is also achieved.