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Table 1 Magic formulas for the rhombic dodecahedron

From: Magic Mathematical Relationships for Nanoclusters

  fcc rhombic dodecahedron n=4
Atoms 8n3+6n2+2n+3, n≥1 odd
   8n3+6n2+2n+1, n≥2 even
  Bonds 48n3+12, n≥1 odd;
   48n3,n≥2 even
  cn=3 8, n ≥2 even
  cn=4 6, n ≥1
  cn=5 12n−12, n ≥1 odd
   12n−24, n ≥2 even
  cn=7 12n2−12n+12, n ≥1
  cn=10 12n−12, n ≥1 odd
   12n, n ≥2 even
  cn=11 12n2−24n+12, n ≥1 odd
   12n2−24n, n ≥2, even
  cn=12 8n3−18n2+14n−3, n ≥1 odd
   8n3−18n2+14n−1,n≥2 even