Table 9 Magic formulas for the 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

\((10t-20)n^2 +(-10t^2+30t-20)n+(\frac{10}{3}t^3-15t^2+\frac{71}{3}t-14),\,n>t\ge 3\)