The paper shows that the essence of mass as a physical phenomenon in N–dimensional space is a consequence of its extension in N+1 space. Leptons and quarks correspond to the symmetry groups of regular polyhedra in three-dimensional space and their mass is given by the volume of the corresponding polyhedron or the sum of the volumes of the corresponding polyhedrons for hadrons. When the particles decay due to the weak interaction, it is possible that one or more quark-antiquark pairs are born, and the symmetry group changes in the form of quark-lepton oscillation. The formulas for the decays of particles are given in a strict form without magical transformations. An attempt is made to systematize all known elementary particles into tables of quark combinations. The masses of all known elementary particles are calculated from the combined polyhedra.