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E. S. Fedorov’s algorithm of the generation of the combinatorial diversity of convex polyhedra: The latest results and applications

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Abstract

E. S. Fedorov’s algorithm allowing us to obtain the full combinatorial diversity of convex polyhedra from the tetrahedron is considered in the paper. The latest results on the number of combinatorially different convex n-hedra for the given n and their point symmetry groups are presented. Possible applications of the results are shown. The problems are formulated, which can be solved at present only by means of powerful computers.

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Authors and Affiliations

  1. Geological Institute, Kola Scientific Center, Russian Academy of Sciences, Apatity, Russia

    Yu. L. Voytekhovsky

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Correspondence to Yu. L. Voytekhovsky.

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To 160th anniversary of Academician E. S. Fedorov and 120th anniversary of its paper “Principles of Morphology and Systematics of Polyhedra”

Original Russian Text © Yu. L. Voytekhovsky.

__________

Translated from Zhurnal Strukturnoi Khimii, Vol. 55, Supplement 1, pp. S111–S125, 2014.

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Voytekhovsky, Y.L. E. S. Fedorov’s algorithm of the generation of the combinatorial diversity of convex polyhedra: The latest results and applications. J Struct Chem 55, 1293–1307 (2014). https://doi.org/10.1134/S0022476614070129

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