E. S. FEDOROV’S ALGORITHM OF THE GENERATION OF THE COMBINATORIAL DIVERSITY OF CONVEX POLYHEDRA: THE LATEST RESULTS AND APPLICATIONS
Yu. L. Voytekhovsky
Geological Institute, Kola Scientific Center, Russian Academy of Sciences, Apatity, Russia
Keywords: convex polyhedron, combinatorial type, Fedorov’s algorithm, point symmetry group, crystallographic and non-crystallographic symmetry groups, combinatorially asymmetric polyhedra, Schlegel projection, systematic and nomenclature of convex polyhedra
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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