Four-dimensional Pyramidal Structure of the Periodic Properties of Atoms and Chemical Elements

The recent results show that the dependence of the elements' properties on the nuclei charge has a four-dimensional structure. The geometrical interpretation of this structure results in a four-dimensional pyramidal representation of the periodic properties of elements, which have traditionally been presented on a plane since Mendeleyev's times. 1. INTRODUCTION. The question whether there is a third dimension in the periodic properties of the elements has been under discussion since 1939. Pauling was first to introduce electronegativity index into the periodic system 1 , while Allen suggested the configuration energy 2. However as Maddox pointed out 3 , neither Pauling nor Allen ever discussed an idea on the existence of three-dimensional invariants and symmetries in the table of elements. The three-dimensional structure that displayed the periodicity of the elemental properties and had the shape of a step pyramid was introduced only in 1992 4. However, it has been recently proven 5 that the structure of the set of all elements has not only the third, but also even the fourth dimension. Below, the four-dimensional properties of the Periodic table are discussed.