Topological Entropies of All 2907 Convex 4- to 9-atomic Polyhedral Clusters

Yury L. Voytekhovsky

Article ID: 514
Vol 2, Issue 1, 2019, Article identifier:

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Abstract


The topological entropy HS of all 2907 convex 4- to 9-atomic polyhedral clusters has been calculated from the point of different symmetrical positions of the atoms. It shows a general trend to drop with growing symmetry of clusters with many local exceptions. The topological entropy HV of the same clusters has been calculated from the point of different valences (chemical bonds) of the atoms. It classifies the variety of clusters in more details. The relationships between the HS and HV entropies are discussed.

Keywords


Convex Polyhedral Clusters; Automorphism Group Orders; Symmetry Point Groups; Chemical Bonds; Topological Entropy

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References


Grünbaum B. Convex polytopes. New York: Springer; 1967.

Voytekhovsky YL, Stepenshchikov DG. Combinatorial crystal morphology. Book 4: Convex polyhedra. Vol. 1: 4- to 12-hedra [Internet]. Apatity: Kola Sci. Centre of RAS. Available at: http://geoksc.apatity.ru/images/stories/Print/ monob /%D0%9A%D0%BD%D0%B8%D0%B3%D0%B0%20IV%20%D0%A2%D0%BE%D0%BC%20I.pdf

Voytekhovsky YL. How to name and order convex polyhedral. Acta Crystallographica Section A: Foundations and Advances 2016; 72: 582–585.

Voytekhovsky YL. Convex polyhedra with minimum and maximum names. Acta Crystallographica Section A: Foundations and Advances 2017; 73: 271–273.

Voytekhovsky YL. Accelerated scattering of convex polyhedral. Acta Crystallographica Section A: Foundations and Advances 2017; 73: 423–425.

Shannon СE. The mathematical theory of communication. The Bell System Technical Journal 1948; 27: 379–423, 623–656.

Halphen E. L’analyse intrinsèque des distributions de probabilité. Publications de l'Institut Statistique de l'Université de Paris 1957; 2: 77–159.




DOI: http://dx.doi.org/10.24294/ace.v2i1.514

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