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Table 13 Magic formulas for the icosahedron

From: Magic Mathematical Relationships for Nanoclusters

  Icosahedron n=4
Atoms \(\frac {10}{3}n^{3} + 5n^{2} + \frac {11}{3}n + 1,~n\ge 1\)
  Bonds 20n3+15n2+7n, n≥1
  cn=6 12, n≥1
  cn=8 30n−30, n≥1
  cn=9 10n2−30n+20, n≥1
  cn=12 \(\frac {10}{3}n^{3} - 5n^{2} + \frac {11}{3}n -1,~n\ge 1\)