“…The classification of pentagonal tilings was completed in a number of cases [4,5,20,28,29], and is expected to be completed soon [22]. Other notable works on spherical tilings include non-edge-to-edge triangular tilings by Dawson and Doyal [15,16,17,18,19] and f -tilings by Avelino, Breda d'Azevedo, Ribeiro, Santos [6,7,8,9,10]. This paper completely classifies edge-to-edge tilings of the sphere by congruent quadrilaterals.…”