Table 8 Magic formulas for the fcc tetrahedron

Atoms

\((\frac{3}{2}t)n^2+(-\frac{9}{2}t^2+6t)n+(\frac{9}{2}t^3-9t^2+\frac{11}{2}t), \,n>t\ge 2\)

Bonds

\((9t-\frac{9}{2})n^2+(-27t^2+45t-\frac{27}{2})n+(27t^3-\frac{135}{2}t^2+\frac{93}{2}t-9),\,n>t\ge 2\)

cn = 3

\(4,\,n>t\ge 2\)

cn = 6

\(6n-6,\,n>t\ge 2\)

cn = 7

\(3n-9t,\,n>t\ge 2\)

cn = 8

\(6,\,n>t\ge 2\)

cn = 9

\(3n^2+(-6t-12)n + (9t^2 +18t-3),\,n>t\ge 2\)

cn = 10

\(6n-18t,\,n>t\ge 2\)

cn = 11

\(3,\,n>t\ge 2\)

cn = 12

\((\frac{3}{2}t-3)n^2 +(-\frac{9}{2}t^2+12t-3)n+(\frac{9}{2}t^3-18t^2+\frac{29}{2}t-4),\,n>t\ge 2\)