Amino acids control the protein folding process and maintain its functional fold. This study underlines the interest of the Laguerre tessellation to determine relevant amino acid volumes in proteins. Previous studies used a limited number of proteins and only buried residues. The present computations improve the method and results on three main points: (i) a large, high-quality updated and refined data bank of proteins is used; (ii) all residues are taken into account, including those at the protein surface, thanks to (iii) the addition of a realistic solvent. The new values of the average and standard deviation of amino acid volumes show significant corrections with respect to previous studies. Another issue of the method is the polyhedral protein/water interface area (PIA) which quantifies the exposure of atoms or residues to the solvent. We propose this PIA as a new, parameter-free, alternative for measuring accessibility. The comparison with NACCESS is satisfactory; however, the methods disagree in pointing out buried residues: where NACCESS evaluates to zero, the exposure given by PIA ranges from 0 to 20%. Variations of average residue volumes have been analyzed under several conditions, e.g., how they depend on protein size and on secondary structure environments. As it is based on strong mathematical grounds and on numerous high-quality protein structures, our work gives a reliable methodology and up-to-date values of amino acid volumes and surface accessibility.