Dataset containing optimized structures of isolated, icosahedral fullerenes, multi-layer fullerene "onions", and stacked graphene layers, organized in folders after types. Graphene structures are also organized after numbers of stacked layers. Optimized using the AIREBO force field in LAMMPS. The file names contain the number of atoms in each structure, the allotrope type, and the force field used (AIREBO). Data consists of standard xyz-structure files with the following structure: Line 1: Number of atoms in the file. Line 2: Comment line containing the potential energy of the optimized structure with the AIREBO force field together with the author list. Line 3 to end of file: Atomic symbol followed by Cartesian coordinates in units of Ångström (Å, 10-10 m).