Construction of fullerenes with the number of hexagons no more than 7 (Q2802651)

A geometric fullerene is defined as the surface of a convex three-dimensional polytope whose facets are all either pentagons or hexagons. Geometric fullerenes are mathematical models of various types of carbon molecules. The author considers sequences of operations (cutting vertex-truncation, edge-truncation, truncation a pair of adjacent edges and the Endo-Kroto operation) which permit to obtain a fullerene from cube and dodecahedron. These constructions are exactly provided in order to obtain fullerenes which have at most seven hexagons.