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Table 19 Magic formulas for the decahedron

From: Magic Mathematical Relationships for Nanoclusters

 

Decahedron n=4

Atoms

\(\frac {5}{6}n^{3} + \frac {5}{2}n^{2}+\frac {8}{3}n +1\)

 

Bonds

\(5n^{3} + \frac {15}{2}n^{2} + \frac {7}{2}n\)

 

cn=4

5, n≥1

 

cn=6

5n−3, n≥1

 

cn=8

10n−10, n≥1

 

cn=9

5n2−15n+10, n≥1

 

cn=12

\(\frac {5}{6}n^{3} - \frac {5}{2}n^{2} + \frac {8}{3}n -1,~n\ge 1\)

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