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Table 13 Magic formulas for the icosahedron

From: Magic Mathematical Relationships for Nanoclusters

 

Icosahedron n=4

Atoms

\(\frac {10}{3}n^{3} + 5n^{2} + \frac {11}{3}n + 1,~n\ge 1\)

 

Bonds

20n3+15n2+7n, n≥1

 

cn=6

12, n≥1

 

cn=8

30n−30, n≥1

 

cn=9

10n2−30n+20, n≥1

 

cn=12

\(\frac {10}{3}n^{3} - 5n^{2} + \frac {11}{3}n -1,~n\ge 1\)

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