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Table 8 Magic formulas for the bcc truncated octahedron

From: Magic Mathematical Relationships for Nanoclusters

  bcc truncated octahedron n=4
Atoms \(8n^{3}+\frac {9}{2}n^{2} +\frac {5}{2},~n\ge 1\) odd
   \(8n^{3}+\frac {9}{2}n^{2} +3n+ 1,~n\ge 2\) even
  Bonds \(56n^{3}-\frac {27}{2}n^{2}-6n+\frac {27}{2},~n\ge 1\) odd
   \(56n^{3}+\frac {27}{2}n^{2}+3n,~n\ge 2\) even
  cn=4 0, n≥1 odd
   6n+12, n≥2 even
  cn=6 24, n≥3 odd
   12n−24, n≥2 even
  cn=7 6n2+12n−34,n≥3 odd
   6n2−12n+8,n≥2 even
  cn=8 6n−6, n≥1 odd; 0, n even
  cn=9 3n2−12n+15, n≥3 odd
   3n2−6n+6, n≥2 even
  cn=10 6n2−12n+6, n≥1 odd
   6n2, n≥2 even
  cn=12 12n−12, n≥1 odd
   6n, n≥2 even
  cn=13 9n2−24n+15, n≥1 odd
   9n2−18n, n≥2 even
  cn=14 \(8n^{3}-\frac {39}{2}n^{2}+18n-\frac {11}{2},~n\ge {1}\) odd
   \(8n^{3}-\frac {39}{2}n^{2}+15n-1,~n\ge {2}\) even