Abstract
The formulas for calculation of the number of atoms in nanoparticles with symmetry group D 6h are reported. The numbers of atoms are determined by six structurally invariant numbers and the “quantum number” of the group order n. Eight classes of nanostructures with symmetry group D 6h are revealed: C ϑ + 12z , where z = 0, 1, 2, …, and C ϑ is C 2, C 6, C 8, or C 14. The sum rule for the coordination numbers of all atoms of subshells related to symmetry elements is established. Two-dimensional nanoparticles are considered.
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