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Table 6 Magic formulas for the fcc cuboctahedron
figure e

From: Magical Mathematical Formulas for Nanoboxes

Cuboctahedron
Atoms \((10t)n^2+(-10t^2+10t)n+(\frac{10}{3}t^3-5t^2+\frac{11}{3}t), \,n>t\ge 3\)
Bonds \((60t-36)n^2+(-60t^2+96t-36)n+(20t^3-48t^2+40t-12),\,n>t\ge 3\)
cn = 5 \(12,\,n>t\ge 2\)
cn = 7 \(24n-24,\,n>t\ge 2\)
cn = 8 \(12n^2+(-12t-12)n +(6t^2+6),\,n>t\ge 2\)
cn = 9 \(8n^2 +(-8t-16)n+(4t^2+4t+8),\,n>t\ge 2\)
cn = 10 \(24n+(-24t),\,n>t\ge 2\)
cn = 11 \(12,\,n>t\ge 2\)
cn = 12 \((10t-20)n^2 +(-10t^2+30t-20)n+(\frac{10}{3}t^3-15t^2+\frac{71}{3}t-14),\,n>t\ge 3\)