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Table 9 Magic formulas for the icosahedron
figure h

From: Magical Mathematical Formulas for Nanoboxes

Icosahedron
Atoms \((10t)n^2+(-10t^2+10t)n+(\frac{10}{3}t^3-5t^2+\frac{11}{3}t), \,n>t\ge 3\)
Bonds \((60t-30)n^2+(-60t^2+90t-30)n+(20t^3-45t^2+37t-12),\,n>t\ge 3\)
cn = 6 \(12,\,n>t\ge 2\)
cn = 8 \(30n-30,\,n>t\ge 2\)
cn = 9 \(20n^2+(-20t-40)n +(10t^2+10t+20),\,n>t\ge 2\)
cn = 10 \(30n+(-30t),\,n>t\ge 2\)
cn = 11 \(12,\,n>t\ge 2\)
cn = 12 \((10t-20)n^2 +(-10t^2+30t-20)n+(\frac{10}{3}t^3-15t^2+\frac{71}{3}t-14),\,n>t\ge 3\)