Plato’s Bodies – Models for some Coordination Compounds in Mathematical Chemistry

Author: Neli Sidamonidze
Co-authors: Mikheil Gverdtsiteli
Annotation:

Plato’s Bodies – regular polyhedrons (tetrahedron, cube, octahedron, dodecahedron, and icosahedrons) are interesting objects from the point of new of mathematical chemistry, as they can be used for modeling of some coordination compounds. Thus the elaboration of algebraic character for these polyhedrons is interesting problem. The representation of tetrahedron in the form of pseudocontiguity (PCM) matrix is: We had modernized PCM matrix – new MPCM has the second rang. The first diagonal elements represents the degree of one edge, the secons – the sum of the degrees of other edges. Nondiagonal elements are the sum of the multiciplities of edges (for tetrahedron three simple edges are considered as one triple edge). Thus, for tetrahedron MPCM has the form: Within thes scape of this approach the algebraic characters of the polyhedrons are the values of the determinants of MPCM. These values are represented below: Δtetr. = 18; Δcube = 54; Δocta. = 64; Δdodec. =162; Δicos. =250. Modeling of the coordination compound containing tetrahedral inner coordination sphve was carried out.