How can the accuracy of the calculated standard heats of formation Delta H-f(0) of fullerenes be improved? How reliable are the values of Delta H-f(0) calculated from hyperhomodesmotic reactions? This work is the first to address these questions. By comparing the results obtained from three hyperhomodesmotic reactions containing only fullerenes, it is illustrated that both the resonance contribution and the strain energy contribution should be considered in the construction of hyperhomodesmotic reactions. An attempt to construct such hyperhomodesmotic reactions for fullerenes has been carried out, and several new insights are indicated.