Beginning with some observations about the periodic and nonperiodic structures commonly adopted by elements in the periodic table, I will introduce a definition ("objective structures") of a mathematically small but physically well represented class of molecular structures. This definition will be seen to have an intimate relation to the invariance of the equations of quantum mechanics. The resulting framework can be used to design various multiscale methods, and gives a new perspective on some of the fundamental solutions in continuum mechanics for solids and fluids. Open mathematical problems will be highlighted.