ABSTRACT
In 1923, D.M.Y.Sommerville [5] classified the edge-to-edge tilings of the sphere with congruent isosceles spherical triangles, with directly congruent spherical triangles, and with congruent spherical triangles subject to the condition that the angles meeting at any vertex of the tiling are congruent. This last condition forces all adjacent pairs of triangles to be mirror images, so that the triangle tiles by repeated reflection.
