Abstract A series of B3LYP/6-31G∗ calculations reveal that the D3 isomer is the most stable isomer of C32 carbon cages. The derivatives of it, including additional productions (C32H2, C32Cl2), hetero-fullerenes (C30B2, C30N2), isoelectronic molecules ( C 30 B 2 2 - , C 30 N 2 2 + ) 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 D3 C32. Our calculations suggest that the building block of C32 oligomers which linked by sp3 bonds should be the saturated C32H2 unit.