Table 6 Magic formulas for the fcc 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

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