Tilings of the Sphere with Right Triangles II: The (1, 3, 2), (0, 2, n) Subfamily

Sommerville [8] and Davies [2] classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper shows that no right triangles in a certain subfamily can tile the sphere, although multilayered tilings are possible.