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TopHigher Dimension Of Polyatomic Molecules As A Result Of The Interaction Of The Electron Orbitals Of Atoms In A Molecule
The most common in biomolecules is a carbon atom, the main role of which to be binding in the center of biomolecules. Consider, for example, ethane molecule CH4. The carbon atom in this molecule binds around four hydrogen atoms. Geometrically, this molecule is a tetrahedron, whose vertices are located of the hydrogen atoms, and in the center is carbon atom. In (Zhizhin G. V., 2015; Zhizhin & Diudea, 2016) it is shown that the dimension of the molecules having the form of a tetrahedron with the center equals 4. Indeed, by calculating the number of vertices, edges, faces and three-dimensional plane in the figure, i.e.
, where i is the dimension of the edge, 0 ≤ i ≤ 3, we find that 
, 
=10, 
= 10, 
= 5. Substituting these values into the Euler equation (Grunbaum, 1967; Zhizhin G.V, 2014), which determines the relationship between these values of polyhedron in any dimension n (polytopes)
(1) we see that the equation (1) is satisfied for
n = 4, i.e. the dimension of the molecule in the form of a tetrahedron with the center is 4.