Skip to main content

Table 12 Magic formulas for the truncated hexagonal bipyramid

From: Magic Mathematical Relationships for Nanoclusters

  Truncated hexagonal bipyramid n=4
Atoms \(\frac {7}{2}n^{3} + \frac {21}{4}n^{2} + \frac {7}{2}n + \frac {3}{4},~n\ge 3\) odd
   \(\frac {7}{2}n^{3} + \frac {21}{4}n^{2} + \frac {7}{2}n + 1,~n\ge 2\) even
  Bonds \(21n^{3} + \frac {27}{2}n^{2} + 3n - \frac {3}{2},~n\ge 3\) odd
   \(21n^{3} + \frac {27}{2}n^{2} + 3n,~n\ge 2\) even
  cn=5 6, n≥2
  cn=6 3n+9, n≥1
  cn=7 18n−24, n≥1
  cn=8 \(\frac {9}{2}n^{2} - 9n + \frac {9}{2},~n \ge {3}\), odd
   \(\frac {9}{2}n^{2} - 9n + 3,~n \ge {2}\), even
  cn=9 6n2−12n+6, n≥3, odd
   6n2−12n+8, n≥2, even
  cn=12 \(\frac {7}{2}n^{3} - \frac {21}{4}n^{2} + \frac {7}{2}n -\frac {3}{4},~n\ge 3\) odd
   \(\frac {7}{2}n^{3} - \frac {21}{4}n^{2} + \frac {7}{2}n -1,~n\ge 2\) even