From circle packing to covering on a sphere with antipodal constraints
作者： P. W. Fowler , T. Tarnai , Zs. Gáspár
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摘要: The problem treated here is: how must N antipodal pairs of equal circles (spherical caps) given angular radius r be arranged on the surface a sphere so that area covered by will as large possible? Conjectured solutions this for = 4,5,7 are where varies from maximum packing to minimum covering radius. These cases exhibit sequences symmetry– and edge–number transitions in contact polyhedra, which, general, differ those unconstrained centrosymmetry is not enforced. New arrangements conjectured 4, 5 7 pairs: they hexagonal bipyramid, D 2h deltahedron cube+octahedron compound, respectively.
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