The packing geometry of amino acids in folded proteins is analyzed via a modified Voronoï tessellation method which distinguishes bulk and surface. From a statistical analysis of the Voronoï cells over 40 representative proteins, it appears that the packings are in average similar to random packings of hard spheres encountered in condensed matter physics, with a quite strong fivefold local symmetry. Moreover, the statistics permits one to establish a classification of amino acids in terms of increasing propensity to be buried in agreement with what is known from chemical considerations.