Abstract

A 4-dimensional periodic table of chemical elements is presented. The 120 elements in the n = 8 system are located on vertices of a 4D-cubic lattice and specified by Cartesian coordinates based on the four quantum numbers. Each quantum number is represented by a vector along a different spatial direction in 4D Euclidean space. The 4D PT has a fixed topology governed by Euler–Poincare-type equation and the chemical elements have a fixed connectivity with neighboring elements within the 4D PT. Various geometric transformations by rotations and elongations of vectors enable morphing of one PT to another in a continuum while preserving the 4D topology. The 4D structure exhibits principles of complementarity and zero-cyclic sum in chemical elements. Complementarity enables the extension to n = 9 elements and beyond. The 4D PT of elements extends to isotopes and also to molecules and compounds with the same underlying principles.