The smallest fullerene, dodecahedral C20, is studied using a one band Hubbard
model parameterized by U/t. Results are obtained using exact diagonalization of
matrices with linear dimensions as large as 5.7 x 10^9, supplemented by quantum
Monte Carlo. We report the magnetic and spectral properties of C20 as a
function of U/t and investigate electronic pair binding. Solid forms of C20 are
studied using cluster perturbation theory and evidence is found for a
metal-insulator transition at U ~ 4t. We also investigate the relevance of
strong correlations to the Jahn-Teller effect in C20.