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Abstract
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In this talk we discuss deep and fruitful inter-relations between different areas of mathematics and applications of these relations.
By a fullerene we mean a combinatorial simple 3-polytope with only pentagonal and hexagonal facets. This is a mathematical model for spherical shaped molecule of carbon with atoms linked into pentagonal and hexagonal rings (1996 Nobel Prize in chemistry to Robert Curl, Harold Kroto and Richard Smalley). The Euler formula implies that any fullerene has p_5=12 pentagons. It can be proved that the number p_6 of hexagons can be arbitrary except for one. The dodecahedron is the only fullerene with p_6=0, while for large p_6 the number of fullerenes grows as p_6^9. We show that there exists a finite set of operations sufficient to construct arbitrary fullerene from the dodecahedron (V.M.Buchstaber, N.Yu.Erochovets, Structural Chemistry, 2016, 1–10).
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