The formation and dynamical properties of D-5d-symmetry self-trapped exciton (STE) derived from the electronic h(u) --> t(1u) parity-forbidden transition of neutral buckyball are studied in the presence of Coulomb interactions using the Bogoliubov-de Gennes formalism. Within the lattice relaxation theory, the multi-mode vibronic structures in the luminescence and absorption spectra related to STEs are elucidated in good agreement with experiments. The STEs arising from the allowed t(1u) --> t(1g) transition of C-60(1-) and C-60(2-) as well as the possibility of forming a self-trapped biexciton (STBE) in C-60(1-) also considered.