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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

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