Present studies in physics assume that elementary particles are the building blocks of all matter, and that they are zero-dimensional objects which do not occupy space. The new I-Theory predicts that elementary particles do indeed have a substructure, three dimensions, and occupy space, being composed of fundamental particles called I-particles. In this article we identify the substructural pattern of elementary particles and define the quanta of energy that form each elementary particle. We demonstrate that the substructure comprises two classes of quanta which we call "attraction quanta" and "repulsion quanta". We create a model that defines the rest-mass energy of each elementary particle and can predict new particles. Lastly, in order to incorporate this knowledge into the contemporary models of science, a revised periodic table is proposed.