Energies on deformed planar lattices. Geometric consideration

The discovery of 2D materials, such as graphenes and fullerenes, sparked a surge of interest in the understanding of their structures and properties. This interest was caused by their electronic and mechanical properties. One approach, used by Friedrich, Seitz and Stefanelli, stems from geometrical considerations with elements of potential theory. We also are interested in the optimal properties of truncated icosahedrons, such as C60. We calculate the coordinates of the points of the icosahedra, as well as its inner distance distribution. This allows direct computation of the energies for arbitrary distance potentials and external fields, which we plan to use during the study of the optimality of different members of the family and hopefully understand why the shape of C60 is what it is.