A graphite-prism definition for Avogadro's "integer"
  The new International System of Units may let us select an integer value for Avogadro's number. Some might prefer an integer that's divisible by 12, so that an integer number of $^{12}C$ atoms may be associated (to first order) with a gram's mass. For educational and practical reasons it may also help to choose a {\em physically-meaningful} definition within measurement error of the current numeric value. Cubes of diamond face-centered-cubic Si and (much rarer) face-centered-cubic C have been proposed, but these structures do not have naturally-occurring facets (or numbers of atoms generally divisible by 12). We show here that graphite prisms formed by stacking $m$ hexagonal graphene sheets, with $m \equiv 51,150,060$ carbon-12 atoms on each side, are a natural solution that may facilitate generation of precise molar standards as well. 
P. Fraundorf and Melanie Lipp
physics.gen-ph