Some New Tilings of the Sphere with Congruent Triangles

Robert J. MacG. Dawson
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 489–496


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.