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The optimal packing of circles on a sphere

Abstract

The closest packing ofx circles on the surface of a sphere is calculated in the same way that the stereochemical arrangement of atoms around a central atom is determined. A number of improved packings have been discovered for x = 19 to 80. A notable feature is that the structures are generally of low symmetry. The packing densityp, defined as the fraction of the spherical surface that is enclosed by the circles, increases only very slowly as the number of circles increases and the values remain substantially below that for a close packed plane, or for an octahedron or icosahedron.

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Clare, B.W., Kepert, D.L. The optimal packing of circles on a sphere. J Math Chem 6, 325–349 (1991). https://doi.org/10.1007/BF01192589

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  • DOI: https://doi.org/10.1007/BF01192589

Keywords

  • Physical Chemistry
  • Spherical Surface
  • Notable Feature
  • Central Atom
  • Close Packing