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Table 3 Magic formulas for the octahedron

From: Magic Mathematical Relationships for Nanoclusters

  fcc octahedron n=6
Atoms \(\frac {2}{3}n^{3} + 2n^{2} + \frac {7}{3}n+1,~n\ge 1\)
  Bonds 4n3+6n2+2n, n≥0
  cn=4 6, n≥1
  cn=7 12n−12, n≥1
  cn=9 4n2−12n+8, n≥1
  cn=12 \(\frac {2}{3}n^{3}-2n^{2}+\frac {7}{3}n-1,~n\ge 1\)