[en] A theorem concerning fermion interaction is postulated and applied to the problems of atomic (electronic) and nuclear physics. Model building based solely upon the postulate that adjacent like fermions must be singlet paired accounts for the closed shells of both nuclear and atomic structure. The implied antiferromagnetic FCC lattice of protons and neutrons in alternating layers has been found by previous workers to be the lowest-energy solid configuration of nuclear matter (N = P). The buildup of the FCC lattice from a central tetrahedron reproduces all of the shells and subshells of the isotropic harmonic oscillator, which is the basis for the shell model. In atomic structure, the singlet pairing of adjacent electrons implies closed-shell structures uniquely at the six noble gases and the three noble metals, Ni, Pd, and Pt. The basis for the postulate concerning fermions is found in terms of classical electrodynamics; it is a microscopic corollary of Biot-Savart's law that parallel currents attract whereas antiparallel currents repel. (author)