Ab initio calculations of 0.01-10 eV collisions of positrons with fullerene C20 are performed using a single-center expansion of the total wave function and a model potential to represent the positron-molecule interaction. Total elastic cross sections and eigenphase sums are generated and analyzed, while bound states and possible long-lifetime scattering resonances are explored, particularly those which are found to reside within the cage structure defined by the carbon atoms of the cluster. 2008 The American Physical Society.