A series of B3LYP/6-31G* calculations reveal that the D-3 isomer is the most stable isomer of C-32 carbon cages. The derivatives of it, including additional productions (C32H2, C32Cl2), hetero-fullerenes (C30B2, C30N2), isoelectronic molecules (C30B22-, C30N22+) and dimers have been investigated at the same level. The results show that, the additional hydrogen atoms and replaced nitrogen atoms can enhance the electronic stabilization of D3C32. Our calculations suggest that the building block of C-32 oligomers which linked by sp(3) bonds should be the saturated C32H2 unit. (c) 2006 Elsevier B.V. All rights reserved.