We study gas and solid phases of C-20 fullerene. By using hybrid density functional theory, we calculate the anion photoelectron spectra of C-20 isomers and assign one of the experimental spectra to the fullerene structure, so we confirm that the C-20 fullerene is really synthesized. We next perform local density approximation calculation on polymerized phases of C-20 fullerene. The most stable system is found to have the orthorhombic structure. Based on calculated electron density of the states, we conclude that the hole-injected sample is a candidate for superconductor.