A systematic survey is performed on all isomers of fullerene C-46 composed of squares, pentagons, hexagons. Density functional calculations demonstrate that the classical isomers generally follow the pentagon adjacency penalty rule. Unexpectedly, a non-classical isomer incorporating a square, i.e., C-46-10-1 is predicted to be more energetically favorable than its lowest-energy classical rival. It is interesting that the non-classical structures with one or two squares exhibit unusually large HOMO-LUMO gaps. The relative thermodynamical stability is evaluated for several low-lying isomers in terms of the Gibbs function. The maximum pyramidization angles are also introduced to evaluate their stability. (C) 2011 Elsevier B.V. All rights reserved.