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Table 6 Magic formulas for the bcc cuboctahedron

From: Magic Mathematical Relationships for Nanoclusters—Errata and Addendum

 

bcc cuboctahedron

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

\(\frac {20}{3}n^{3}+19n^{2}+\frac {64}{3}n+9,n\ge 1\) odd

  

\(\frac {20}{3}n^{3}+19n^{2}+\frac {46}{3}n,~n\ge 2\) even

 

cn=2

12, n≥1 odd; 0, n even

 

cn=3

12n−12, n≥1 odd; 0, n even

 

cn=4

4n2−4n+6, n≥1 odd

  

4n2+8n, n≥2 even

 

cn=6

0, n≥1 odd; 12, n even

 

cn=7

2n2+4n+2, n≥1 odd

  

2n2+4n−16, n≥2 even

 

cn=8

\(\frac {5}{3}n^{3}+1n^{2}-\frac {2}{3}n-1,~n\ge {1}\) odd

bcc cuboctahedron n=2

 

\(\frac {5}{3}n^{3}+1n^{2}-\frac {11}{3}n+5,~n\ge {2}\) even

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