Symmetry in nature: discreteness, three-dimensional extension, motion, and minimum potential energy

At every scale of Nature symmetry manifests in many ways, under many guises, and apparently disjoint descriptions, from Platonic solids and the Fibonacci sequence, to modern charge, parity, and time invariance. It is posited here that discreteness, three-dimensional extension, motion, and minimization of potential energy may be common traits and principles leading to observed symmetries. In 1986 this author found that, when driven by an inverse potential field, N discrete punctual particles array on the surface and inside a sphere in highly symmetrical configurations exhibiting tangential equilibrium and low potential energy. We add here new constraints and boundary conditions arising from three-dimensional extension and motion of the discrete corpuscles within the symmetrical N-particle arrays (2 < N < 20).