Three-dimensionality of space in the structure of the periodic table of chemical elements

The effect of the dimension of the 3D homogeneous and isotropic Euclidean space, and the electron spin on the self-organization of the electron systems of atoms of chemical elements is considered. It is shown that the finite dimension of space creates the possibility of periodicity in the structure of an electron cloud, while the value of the dimension determines the number of stable systems of electrons at different levels of the periodic table of chemical elements and some characteristics of the systems. The conditions for the stability of systems of electrons and the electron system of an atom as a whole are considered. On the basis of the results obtained, comparison with other hierarchical systems (nanostructures and biological structures) is performed.