**4.1. Atom and Nanovoids in the polyhedron model of an ideal crystal**

The idea of providing the coordination polyhedron in a crystal belongs to L. Pauling. N. V. Belov identified more complex and less symmetric forms of coordination polyhedra than the octahedron and the tetrahedron. As a further development of the polyhedron method of presentation for the crystal, one can consider the idea of the image of the coordination polyhedron combinations of simple forms [45] because through these combinations it is possible to explain the role of voids in the polyhedral models of crystal structures.

Using examples of the structures of periclase, sphalerite, wurtzite, fluorite, rutile, anatase, brookite, nickeline, barite, stannum, hydrargyrum, copper, and magnesium the following regularity is found:


So, the concept regarding coordination vacancies that are unpopulated vertices and the faces of coordination simple forms is formulated. Coordination vacancy may coincide with the host lattice or it can be in the interstitial space. In the first case, the filling or the formation of coordination vacancies leads ultimately to a change in the symmetry of the structure. As an example, we can look at the structural transition in the system Ni-As. In the second case, coordination vacancies can be populated with impurity atoms (diamond) or extra electrons of π-bound (graphite) and unattributed electron pairs (litharge).
