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Table 7 Magic formulas for the fcc octahedron
figure f

From: Magical Mathematical Formulas for Nanoboxes

fcc octahedron

Atoms

\((4t)n^2+(-8t^2+8t)n+(\frac{16}{3}t^3-8t^2+\frac{14}{3}t), \,n>t\ge 2\)

Bonds

\((24t-12)n^2+(-48t^2+72t-24)n+(32t^3-72t^2+52t-12),\,n>t\ge 2\)

cn = 4

\(6,\,n>t\ge 2\)

cn = 7

\(12n-12,\,n>t\ge 2\)

cn = 9

\(8n^2+(-16t-8)n+(16t^2-8t+8),\,n>t\ge 2\)

cn = 11

\(12n +(-24t +12),\,n>t\ge 2\)

cn = 12

\((4t-8)n^2 +(-8t^2+24t-16)n+(\frac{16}{3}t^3-24t^2+\frac{110}{3}t-14),\,n>t\ge 2\)

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