Regularities of Coordination Spheres in the Crystal Lattice of the Cubic Symmetry

A procedure that allows us to describe the distribution patterns of atomic sites of the diamond type structure over the coordination spheres is presented. The spatial packing of the coordination spheres is formed by the vertices of the seven base polyhedra with cubic symmetry and the four polyhedra with tetrahedral symmetry. The former is given by a set of the seven regular or semi-regular polyhedra of Platonic and Archimedean solids such as the cube, the truncated cube, the octahedron, the cubic-, truncated-, rhomboidal-, and truncated cubic octahedrons. The latter is given by a set of four other shapes such as the tetrahedron, the rhombohedral-, truncated-, and truncated rhombohedral tetrahedrons.