Goldberg–Coxeter construction
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The Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs with degree 3 or 4.[1][2] It also applies to the dual graph of these graphs, i.e. graphs with triangular or quadrilateral "faces". The GC construction can be thought of as subdividing the faces of a polyhedron with a lattice of triangular, square, or hexagonal polygons, possibly skewed with regards to the original face: it is an extension of concepts introduced by the Goldberg polyhedra and geodesic polyhedra. The GC construction is primarily studied in organic chemistry for its application to fullerenes,[1][2] but it has been applied to nanoparticles,[3] computer-aided design,[4] basket weaving,[5][6] and the general study of graph theory and polyhedra.[7]
The Goldberg–Coxeter construction may be denoted as , where is the graph being operated on, and are integers, , and .