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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

\(\frac {2}{3}n^{3}-2n^{2}+\frac {7}{3}n-1,~n\ge 1\)

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