Skip to main content

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