ABSTRACT
The tetrahedral dual coordinate system (TDCS) is found within the atomic structure of square and triangular grid planes of crystallography as Miller lattice system, and in organic stereochemistry compounds with tetrahedral and ligand bonding. The TDCS derived by applying four triangular algebraic planes to the tetrahedron of organic chemistry with six edges, represented algebraically as (r, s, t, u, v, w). These edges become six number lines with six directions in atomic space as six dimensions (6D). There is a need for a TDCS with extra dimensions to describe the recent theories such as six and ten-dimensional string theory. Six-dimension theory includes the merging of four equilateral triangular grids with three orthogonal (x, y, z) axes of symmetry, geometrically modeled on the cuboctahedron. Duals rhombic dodecahedron and cuboctahedron are geometrically related to (6D) cuboctahedron model. Polyhedron duals have an interchangeable relationship between faces and vertices or vertices and edges.
