Some New Tilings of the Sphere with Congruent Triangles

Robert J. MacG Dawson

Many years ago, Sommerville classified the tilings of the sphere with congruent spherical triangles ? under some assumptions. Later, Davies did the same, under only the restriction that the triangles should meet edge-to-edge. This paper surveys a recently-discovered class of tilings with congruent spherical triangle tiles that do not meet edge-to-edge.