APS/Alan Stonebraker; Image of polytope on homepage Wikimedia Commons/Maxim Razin

Figure 1: (Left) The electronic configuration of an atom (oxygen is shown here) is based on Pauli’s exclusion principle. (Right) A schematic showing that the generalized Pauli constraints restrict the natural occupation numbers $ni$, $nj$ to the dark-blue polygon, significantly strengthening Pauli’s exclusion principle (light-blue square).