The periodic table is among the most widely used tools in both physics and chemistry. Over the years, hundreds of different versions have been proposed, and numerous books have been devoted to its design and interpretation. Broadly, these periodic tables can be grouped into two main categories. The first traces back to Klechkowski’s proposal, which emphasizes valence periodicity. The second—and by far the most familiar—is the modern table organized according to the electronic configurations of atoms.

Despite their pedagogical value, these representations still exhibit important limitations. First, there are nearly twenty exceptions among the experimentally well-established electronic configurations of the elements. No version of the periodic table is able to distinguish these cases by placing the elements in a position that reflects their actual electronic configuration.Second, the standard table does not adequately capture the variety of valences that a single element can exhibit. Together, these shortcomings restrict the usefulness of the traditional periodic table for chemists, especially in teaching contexts.