Chemical Compound Structures and the Higher Dimension of Molecules by Gennadiy Vladimirovich Zhizhin

Author:Gennadiy Vladimirovich Zhizhin
Language: eng
Format: epub
Publisher: IGI Global

Table 2 lists the edges of the graph and the corresponding triangular faces of the nine tetrahedrons along which these tetrahedrons contact each other.

Since each face of nine tetrahedrons is closed by the face of some other tetrahedron of the indicated set of tetrahedrons, the figure made up of these tetrahedrons is closed and represents a certain polytope. Constructing the projection of this polytope onto a two-dimensional plane leads to the proof that each of the six vertices of nine tetrahedrons is connected by edges with the all other vertices. Therefore, the projection onto the two-dimensional plane of this polytope coincides with the projection of the five-dimensional regular simplex (Zhizhin, 2014) onto the two-dimensional plane (Figure 13).

Figure 13. Polytope with hyper- faces of tetrahedrons 1, 2, 3, 4, 5, 6, 7, 8, 9

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