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Table 9 Magic formulas for the bcc cuboctahedron

From: Magic Mathematical Relationships for Nanoclusters

  bcc cuboctahedron n=3
Atoms \(\frac {5}{3}n^{3}+7n^{2}+\frac {34}{3}n+7,~n\ge 1\) odd
   \(\frac {5}{3}n^{3}+7n^{2}+\frac {25}{3}n+1,~n\ge 2\) even
  Bonds \(\frac {35}{3}n^{3}+34n^{2}+\frac {112}{3}n+15,n\ge 1\) odd
   \(\frac {35}{3}n^{3}+34n^{2}+\frac {67}{3}n,~n\ge 2\) even
  cn=4 12, n≥1 odd; 0, n even
  cn=6 12n−12, n≥1 odd; 0, n even
  cn=7 n2−4n+3, n≥1 odd
   n2+14n, n≥2 even
  cn=9 3n2+3, n≥1 odd
   3n2−6n, n≥2 even
  cn=10 n2+4n+3, n≥1, odd
   n2−2n+12, n≥2, even
  cn=12 12n−24, n≥2 even; 0, n odd
  cn=13 4n2−4, n≥3 odd
   4n2−12n+14, n≥2 even
  cn=14 \(\frac {5}{3}n^{3}-2n^{2}-\frac {2}{3}n+2,~n\ge {1}\) odd
   \(\frac {5}{3}n^{3}-2n^{2}+\frac {7}{3}n-1,~n\ge {2}\) even