The production and isolation of small fullerenes and of their stable c
ompounds and the knowledge of their chemistry should pave the way to t
he syntesis of novel carbon-based cluster-assembled materials like car
bon clathrates, hollow diamonds and diamond-like thin films. In this q
uest, the knowledge of the valence of the small fullerenes is essentia
l. We report here that the small fullerenes C-n (20 less than or equal
to n less than or equal to 32), aside from the well known values asso
ciated with the local one electron picture of dangling bonds, display
hidden valences connected with the free electron picture of the shell
structure of pi-electrons.