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Mathematical Design of Nanomaterials From Clusters of Higher Dimension
Abstract
Using concrete examples of clusters of chemical compounds of various types (intermetallic clusters, metal chains with ligands, polyhedral metal clusters with ligands), it is shown how nanomaterials are formed from individual clusters by multiplying their geometric structure by other geometric elements of different dimensions. The considered examples correspond to nanomaterials with a structure of limited complexity. However, the mathematical apparatus developed on the basis of the geometry of high-dimensional polytopes allows, in principle, to describe and study and design nanomaterials of this type of any complexity and any dimension. In particular, nanomaterials with the simultaneous use of elements with different metric characteristics can be attributed to such nanomaterials.
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