The periodic depictions of the natural system of elements produced by Mendeleyev and his contemporaries were based on atomic mass A and chemical valence G of the elements then already discovered. In their and in later more refined periodic tables the periodicity was initially highlighted for values of G from 0 to 8; but long tables with 18 groups were soon required to account for the growing number of elements and their chemical properties. The atomic masses (co-determined by the assorted isotopes of an element) were replaced by the atomic number Z. The current knowledge of the electronic states of atoms and molecules now calls for a standard form of the periodic table which reflects the large energy gaps between the noble-gas (sp) 8 core shells and the electronic open spdf valence shells, which physically determine the chemical periodicity of rows with lengths increasing in double-steps. A graphic representation as introduced in IUPAC's Red Book has served well for education and research in chemistry. There is presently no need for graphical or other changes, but existing "irregularities" of single atoms or groups of atoms, mainly those of higher values of Z, require dedicated considerations based on the laws of physics which allow to rationalize unexpected deviations from the Aufbau principle and other rules-of-thumb.